Elektrodinamika kuantiko - Wikipedia, entziklopedia askea.

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hartu Wikimedia Estoniak jarritako erronkan.\u003C/center\u003E\u003C/div\u003E\n\u003Cdiv style=\"clear:both;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Gunea"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Edukiak" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Edukiak</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ezkutatu</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">⇑ Gora</div> </a> </li> <li id="toc-Historia_eta_iragarpenak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historia_eta_iragarpenak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Historia eta iragarpenak</span> </div> </a> <ul id="toc-Historia_eta_iragarpenak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Teoriaren_deskribapena" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Teoriaren_deskribapena"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Teoriaren deskribapena</span> </div> </a> <button aria-controls="toc-Teoriaren_deskribapena-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Teoriaren deskribapena azpiatal</span> </button> <ul id="toc-Teoriaren_deskribapena-sublist" class="vector-toc-list"> <li id="toc-Formalismoa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formalismoa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Formalismoa</span> </div> </a> <ul id="toc-Formalismoa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tokiko_'"`UNIQ--postMath-00000007-QINU`"'_neurgailuaren_aldaezintasuna" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tokiko_'"`UNIQ--postMath-00000007-QINU`"'_neurgailuaren_aldaezintasuna"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Tokiko '"`UNIQ--postMath-00000007-QINU`"' neurgailuaren aldaezintasuna</span> </div> </a> <ul id="toc-Tokiko_'"`UNIQ--postMath-00000007-QINU`"'_neurgailuaren_aldaezintasuna-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Egokitasun_esperimentala" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Egokitasun_esperimentala"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Egokitasun esperimentala</span> </div> </a> <ul id="toc-Egokitasun_esperimentala-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Formulazio_matematikoa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formulazio_matematikoa"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Formulazio matematikoa</span> </div> </a> <button aria-controls="toc-Formulazio_matematikoa-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Formulazio matematikoa azpiatal</span> </button> <ul id="toc-Formulazio_matematikoa-sublist" class="vector-toc-list"> <li id="toc-Higidura-ekuazioak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Higidura-ekuazioak"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Higidura-ekuazioak</span> </div> </a> <ul id="toc-Higidura-ekuazioak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Feynmanen_arauak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Feynmanen_arauak"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Feynmanen arauak</span> </div> </a> <ul id="toc-Feynmanen_arauak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Birnormalizazioa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Birnormalizazioa"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Birnormalizazioa</span> </div> </a> <ul id="toc-Birnormalizazioa-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Erreferentziak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Erreferentziak"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Erreferentziak</span> </div> </a> <ul id="toc-Erreferentziak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bibliografia</span> </div> </a> <button aria-controls="toc-Bibliografia-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Bibliografia azpiatal</span> </button> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> <li id="toc-Liburuak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liburuak"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Liburuak</span> </div> </a> <ul id="toc-Liburuak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aldizkariak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aldizkariak"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Aldizkariak</span> </div> </a> <ul id="toc-Aldizkariak-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Kanpo_estekak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kanpo_estekak"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Kanpo estekak</span> </div> </a> <ul id="toc-Kanpo_estekak-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Edukiak" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Eduki-taula" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Eduki taularen ikusgarritasuna aldatu" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Eduki taularen ikusgarritasuna aldatu</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Elektrodinamika kuantiko</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Joan beste hizkuntza batean idatzitako artikulu batera. 56 hizkuntzatan eskuragarri." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-56" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">56 hizkuntza</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Quantenelektrodynamik" title="Quantenelektrodynamik – Suitzako alemana" lang="gsw" hreflang="gsw" data-title="Quantenelektrodynamik" data-language-autonym="Alemannisch" data-language-local-name="Suitzako alemana" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D9%87%D8%B1%D9%88%D8%AF%D9%8A%D9%86%D8%A7%D9%85%D9%8A%D9%83%D8%A7_%D9%83%D9%85%D9%8A%D8%A9" title="كهروديناميكا كمية – arabiera" lang="ar" hreflang="ar" data-title="كهروديناميكا كمية" data-language-autonym="العربية" data-language-local-name="arabiera" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Electrodin%C3%A1mica_cu%C3%A1ntica" title="Electrodinámica cuántica – asturiera" lang="ast" hreflang="ast" data-title="Electrodinámica cuántica" data-language-autonym="Asturianu" data-language-local-name="asturiera" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%B0%D0%B2%D0%B0%D1%8F_%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Квантавая электрадынаміка – bielorrusiera" lang="be" hreflang="be" data-title="Квантавая электрадынаміка" data-language-autonym="Беларуская" data-language-local-name="bielorrusiera" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0_%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Квантова електродинамика – bulgariera" lang="bg" hreflang="bg" data-title="Квантова електродинамика" data-language-autonym="Български" data-language-local-name="bulgariera" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B5%E0%A4%BE%E0%A4%82%E0%A4%9F%E0%A4%AE_%E0%A4%87%E0%A4%B2%E0%A5%87%E0%A4%95%E0%A5%8D%E0%A4%9F%E0%A5%8D%E0%A4%B0%E0%A5%8B%E0%A4%A1%E0%A4%BE%E0%A4%AF%E0%A4%A8%E0%A5%88%E0%A4%AE%E0%A4%BF%E0%A4%95%E0%A5%8D%E0%A4%B8" title="क्वांटम इलेक्ट्रोडायनैमिक्स – Bhojpuri" lang="bh" hreflang="bh" data-title="क्वांटम इलेक्ट्रोडायनैमिक्स" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8B%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%9F%E0%A6%BE%E0%A6%AE_%E0%A6%A4%E0%A6%A1%E0%A6%BC%E0%A6%BF%E0%A7%8E-%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="কোয়ান্টাম তড়িৎ-গতিবিজ্ঞান – bengalera" lang="bn" hreflang="bn" data-title="কোয়ান্টাম তড়িৎ-গতিবিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="bengalera" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kvantna_elektrodinamika" title="Kvantna elektrodinamika – bosniera" lang="bs" hreflang="bs" data-title="Kvantna elektrodinamika" data-language-autonym="Bosanski" data-language-local-name="bosniera" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Electrodin%C3%A0mica_qu%C3%A0ntica" title="Electrodinàmica quàntica – katalana" lang="ca" hreflang="ca" data-title="Electrodinàmica quàntica" data-language-autonym="Català" data-language-local-name="katalana" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kvantov%C3%A1_elektrodynamika" title="Kvantová elektrodynamika – txekiera" lang="cs" hreflang="cs" data-title="Kvantová elektrodynamika" data-language-autonym="Čeština" data-language-local-name="txekiera" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kvanteelektrodynamik" title="Kvanteelektrodynamik – daniera" lang="da" hreflang="da" data-title="Kvanteelektrodynamik" data-language-autonym="Dansk" data-language-local-name="daniera" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Quantenelektrodynamik" title="Quantenelektrodynamik – alemana" lang="de" hreflang="de" data-title="Quantenelektrodynamik" data-language-autonym="Deutsch" data-language-local-name="alemana" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B2%CE%B1%CE%BD%CF%84%CE%B9%CE%BA%CE%AE_%CE%B7%CE%BB%CE%B5%CE%BA%CF%84%CF%81%CE%BF%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CE%AE" title="Κβαντική ηλεκτροδυναμική – greziera" lang="el" hreflang="el" data-title="Κβαντική ηλεκτροδυναμική" data-language-autonym="Ελληνικά" data-language-local-name="greziera" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="artikulu onak"><a href="https://en.wikipedia.org/wiki/Quantum_electrodynamics" title="Quantum electrodynamics – ingelesa" lang="en" hreflang="en" data-title="Quantum electrodynamics" data-language-autonym="English" data-language-local-name="ingelesa" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kvantuma_elektrodinamiko" title="Kvantuma elektrodinamiko – esperantoa" lang="eo" hreflang="eo" data-title="Kvantuma elektrodinamiko" data-language-autonym="Esperanto" data-language-local-name="esperantoa" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Electrodin%C3%A1mica_cu%C3%A1ntica" title="Electrodinámica cuántica – gaztelania" lang="es" hreflang="es" data-title="Electrodinámica cuántica" data-language-autonym="Español" data-language-local-name="gaztelania" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kvantelektrod%C3%BCnaamika" title="Kvantelektrodünaamika – estoniera" lang="et" hreflang="et" data-title="Kvantelektrodünaamika" data-language-autonym="Eesti" data-language-local-name="estoniera" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9_%DA%A9%D9%88%D8%A7%D9%86%D8%AA%D9%88%D9%85%DB%8C" title="الکترودینامیک کوانتومی – persiera" lang="fa" hreflang="fa" data-title="الکترودینامیک کوانتومی" data-language-autonym="فارسی" data-language-local-name="persiera" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kvanttis%C3%A4hk%C3%B6dynamiikka" title="Kvanttisähködynamiikka – finlandiera" lang="fi" hreflang="fi" data-title="Kvanttisähködynamiikka" data-language-autonym="Suomi" data-language-local-name="finlandiera" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89lectrodynamique_quantique" title="Électrodynamique quantique – frantsesa" lang="fr" hreflang="fr" data-title="Électrodynamique quantique" data-language-autonym="Français" data-language-local-name="frantsesa" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Leictridinimic_chandamach" title="Leictridinimic chandamach – irlandera" lang="ga" hreflang="ga" data-title="Leictridinimic chandamach" data-language-autonym="Gaeilge" data-language-local-name="irlandera" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Electrodin%C3%A1mica_cu%C3%A1ntica" title="Electrodinámica cuántica – galiziera" lang="gl" hreflang="gl" data-title="Electrodinámica cuántica" data-language-autonym="Galego" data-language-local-name="galiziera" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%A7%D7%98%D7%A8%D7%95%D7%93%D7%99%D7%A0%D7%9E%D7%99%D7%A7%D7%94_%D7%A7%D7%95%D7%95%D7%A0%D7%98%D7%99%D7%AA" title="אלקטרודינמיקה קוונטית – hebreera" lang="he" hreflang="he" data-title="אלקטרודינמיקה קוונטית" data-language-autonym="עברית" data-language-local-name="hebreera" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B5%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%9F%E0%A4%AE_%E0%A4%B5%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4%E0%A5%8D%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="क्वाण्टम विद्युत्गतिकी – hindia" lang="hi" hreflang="hi" data-title="क्वाण्टम विद्युत्गतिकी" data-language-autonym="हिन्दी" data-language-local-name="hindia" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kvantna_elektrodinamika" title="Kvantna elektrodinamika – kroaziera" lang="hr" hreflang="hr" data-title="Kvantna elektrodinamika" data-language-autonym="Hrvatski" data-language-local-name="kroaziera" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kvantum-elektrodinamika" title="Kvantum-elektrodinamika – hungariera" lang="hu" hreflang="hu" data-title="Kvantum-elektrodinamika" data-language-autonym="Magyar" data-language-local-name="hungariera" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%94%D5%BE%D5%A1%D5%B6%D5%BF%D5%A1%D5%B5%D5%AB%D5%B6_%D5%A7%D5%AC%D5%A5%D5%AF%D5%BF%D6%80%D5%A1%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1" title="Քվանտային էլեկտրադինամիկա – armeniera" lang="hy" hreflang="hy" data-title="Քվանտային էլեկտրադինամիկա" data-language-autonym="Հայերեն" data-language-local-name="armeniera" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Elektrodinamika_kuantum" title="Elektrodinamika kuantum – indonesiera" lang="id" hreflang="id" data-title="Elektrodinamika kuantum" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiera" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Elettrodinamica_quantistica" title="Elettrodinamica quantistica – italiera" lang="it" hreflang="it" data-title="Elettrodinamica quantistica" data-language-autonym="Italiano" data-language-local-name="italiera" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E9%9B%BB%E7%A3%81%E5%8A%9B%E5%AD%A6" title="量子電磁力学 – japoniera" lang="ja" hreflang="ja" data-title="量子電磁力学" data-language-autonym="日本語" data-language-local-name="japoniera" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%95%E1%83%90%E1%83%9C%E1%83%A2%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%94%E1%83%9A%E1%83%94%E1%83%A5%E1%83%A2%E1%83%A0%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%90" title="კვანტური ელექტროდინამიკა – georgiera" lang="ka" hreflang="ka" data-title="კვანტური ელექტროდინამიკა" data-language-autonym="ქართული" data-language-local-name="georgiera" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%96%91%EC%9E%90_%EC%A0%84%EA%B8%B0%EC%97%AD%ED%95%99" title="양자 전기역학 – koreera" lang="ko" hreflang="ko" data-title="양자 전기역학" data-language-autonym="한국어" data-language-local-name="koreera" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D1%82%D1%8B%D0%BA_%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Кванттык электродинамика – kirgizera" lang="ky" hreflang="ky" data-title="Кванттык электродинамика" data-language-autonym="Кыргызча" data-language-local-name="kirgizera" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kvantin%C4%97_elektrodinamika" title="Kvantinė elektrodinamika – lituaniera" lang="lt" hreflang="lt" data-title="Kvantinė elektrodinamika" data-language-autonym="Lietuvių" data-language-local-name="lituaniera" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Квантна електродинамика – mazedoniera" lang="mk" hreflang="mk" data-title="Квантна електродинамика" data-language-autonym="Македонски" data-language-local-name="mazedoniera" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Elektrodinamik_kuantum" title="Elektrodinamik kuantum – malaysiera" lang="ms" hreflang="ms" data-title="Elektrodinamik kuantum" data-language-autonym="Bahasa Melayu" data-language-local-name="malaysiera" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kwantumelektrodynamica" title="Kwantumelektrodynamica – nederlandera" lang="nl" hreflang="nl" data-title="Kwantumelektrodynamica" data-language-autonym="Nederlands" data-language-local-name="nederlandera" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kvanteelektrodynamikk" title="Kvanteelektrodynamikk – nynorsk (norvegiera)" lang="nn" hreflang="nn" data-title="Kvanteelektrodynamikk" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk (norvegiera)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kvanteelektrodynamikk" title="Kvanteelektrodynamikk – bokmål (norvegiera)" lang="nb" hreflang="nb" data-title="Kvanteelektrodynamikk" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål (norvegiera)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%81%E0%A8%86%E0%A8%82%E0%A8%9F%E0%A8%AE_%E0%A8%87%E0%A8%B2%E0%A9%88%E0%A8%95%E0%A8%9F%E0%A9%8D%E0%A8%B0%E0%A9%8B%E0%A8%A1%E0%A8%BE%E0%A8%87%E0%A8%A8%E0%A8%BE%E0%A8%AE%E0%A8%BF%E0%A8%95%E0%A8%B8" title="ਕੁਆਂਟਮ ਇਲੈਕਟ੍ਰੋਡਾਇਨਾਮਿਕਸ – punjabera" lang="pa" hreflang="pa" data-title="ਕੁਆਂਟਮ ਇਲੈਕਟ੍ਰੋਡਾਇਨਾਮਿਕਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabera" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Elektrodynamika_kwantowa" title="Elektrodynamika kwantowa – poloniera" lang="pl" hreflang="pl" data-title="Elektrodynamika kwantowa" data-language-autonym="Polski" data-language-local-name="poloniera" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Eletrodin%C3%A2mica_qu%C3%A2ntica" title="Eletrodinâmica quântica – portugesa" lang="pt" hreflang="pt" data-title="Eletrodinâmica quântica" data-language-autonym="Português" data-language-local-name="portugesa" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Electrodinamic%C4%83_cuantic%C4%83" title="Electrodinamică cuantică – errumaniera" lang="ro" hreflang="ro" data-title="Electrodinamică cuantică" data-language-autonym="Română" data-language-local-name="errumaniera" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0%D1%8F_%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Квантовая электродинамика – errusiera" lang="ru" hreflang="ru" data-title="Квантовая электродинамика" data-language-autonym="Русский" data-language-local-name="errusiera" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kvantna_elektrodinamika" title="Kvantna elektrodinamika – serbokroaziera" lang="sh" hreflang="sh" data-title="Kvantna elektrodinamika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroaziera" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Quantum_electrodynamics" title="Quantum electrodynamics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Quantum electrodynamics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kvantov%C3%A1_elektrodynamika" title="Kvantová elektrodynamika – eslovakiera" lang="sk" hreflang="sk" data-title="Kvantová elektrodynamika" data-language-autonym="Slovenčina" data-language-local-name="eslovakiera" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Elektrodinamika_kuantike" title="Elektrodinamika kuantike – albaniera" lang="sq" hreflang="sq" data-title="Elektrodinamika kuantike" data-language-autonym="Shqip" data-language-local-name="albaniera" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Квантна електродинамика – serbiera" lang="sr" hreflang="sr" data-title="Квантна електродинамика" data-language-autonym="Српски / srpski" data-language-local-name="serbiera" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kvantelektrodynamik" title="Kvantelektrodynamik – suediera" lang="sv" hreflang="sv" data-title="Kvantelektrodynamik" data-language-autonym="Svenska" data-language-local-name="suediera" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kuantum_elektrodinami%C4%9Fi" title="Kuantum elektrodinamiği – turkiera" lang="tr" hreflang="tr" data-title="Kuantum elektrodinamiği" data-language-autonym="Türkçe" data-language-local-name="turkiera" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0_%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Квантова електродинаміка – ukrainera" lang="uk" hreflang="uk" data-title="Квантова електродинаміка" data-language-autonym="Українська" data-language-local-name="ukrainera" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_%C4%91%E1%BB%99ng_l%E1%BB%B1c_h%E1%BB%8Dc_l%C6%B0%E1%BB%A3ng_t%E1%BB%AD" title="Điện động lực học lượng tử – vietnamera" lang="vi" hreflang="vi" data-title="Điện động lực học lượng tử" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamera" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kwantum_elektrodinamika" title="Kwantum elektrodinamika – warayera" lang="war" hreflang="war" data-title="Kwantum elektrodinamika" data-language-autonym="Winaray" data-language-local-name="warayera" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-zh badge-Q17437798 badge-goodarticle mw-list-item" title="artikulu onak"><a href="https://zh.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E9%9B%BB%E5%8B%95%E5%8A%9B%E5%AD%B8" title="量子電動力學 – txinera" lang="zh" hreflang="zh" data-title="量子電動力學" data-language-autonym="中文" data-language-local-name="txinera" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E9%9B%BB%E5%8B%95%E5%8A%9B%E5%AD%B8" title="量子電動力學 – 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class="mw-content-ltr mw-parser-output" lang="eu" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Feynmandiagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Feynmandiagram.svg/250px-Feynmandiagram.svg.png" decoding="async" width="250" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Feynmandiagram.svg/500px-Feynmandiagram.svg.png 1.5x" data-file-width="722" data-file-height="495" /></a><figcaption> <a href="/wiki/Fotoi" title="Fotoi">Fotoi</a> baten trukeak sortutako bi <a href="/wiki/Elektroi" title="Elektroi">elektroien</a> arteko elkarrekintza erakusten duen Feynman-en diagrama . Diagrama mota horiek garrantzitsuak dira EDCren kalkuluak bideratzeko.</figcaption></figure> <p><b><a href="/wiki/Partikulen_fisika" title="Partikulen fisika">Partikulen fisikan</a></b>, <a class="mw-selflink selflink">elektrodinamika kuantikoa</a> (QED) elektrodinamikaren <a href="/wiki/Eremu-teoria_kuantiko" title="Eremu-teoria kuantiko">eremu kuantikoaren</a> <a href="/wiki/Erlatibitatearen_teoria" title="Erlatibitatearen teoria">erlatibitatearen teoria</a> da. Funtsean, <a href="/wiki/Argi" title="Argi">argiak</a> eta <a href="/wiki/Materia" title="Materia">materiak</a> elkarri nola eragiten dioten deskribatzen du, eta <a href="/wiki/Mekanika_kuantiko" title="Mekanika kuantiko">mekanika kuantikoaren</a> eta <a href="/wiki/Erlatibitate_berezia" title="Erlatibitate berezia">erlatibitate bereziaren</a> arteko erabateko adostasuna lortzen den lehen teoria da. QEDek matematikoki deskribatzen ditu <a href="/wiki/Fotoi" title="Fotoi">fotoien</a> trukearen bidez elkarreragiten duten <a href="/wiki/Karga_elektriko" title="Karga elektriko">elektrikoki kargatutako</a> partikulekin zerikusia duten <a href="/wiki/Fenomeno" title="Fenomeno">fenomeno</a> guztiak, eta elektromagnetismo klasikoaren kontrapartida kuantikoa irudikatzen du, materiaren eta argiaren arteko elkarrekintzaren berri osoa emanez. </p><p>Termino teknikoetan, QED huts kuantiko elektromagnetikoaren perturbazioaren teoria gisa deskriba daiteke. <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynmanek</a> <i>fisikaren harribitxia</i> deitu zion, elektroiaren une magnetiko anomaloa eta hidrogenoaren energia-mailen Lamb-en aldaketa bezalako kantitateen iragarpen oso zehatzengatik<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historia_eta_iragarpenak">Historia eta iragarpenak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=1" title="Aldatu atal hau: «Historia eta iragarpenak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=1" title="Edit section's source code: Historia eta iragarpenak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Feynman_and_Oppenheimer_at_Los_Alamos.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Feynman_and_Oppenheimer_at_Los_Alamos.jpg/250px-Feynman_and_Oppenheimer_at_Los_Alamos.jpg" decoding="async" width="250" height="202" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Feynman_and_Oppenheimer_at_Los_Alamos.jpg/375px-Feynman_and_Oppenheimer_at_Los_Alamos.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Feynman_and_Oppenheimer_at_Los_Alamos.jpg/500px-Feynman_and_Oppenheimer_at_Los_Alamos.jpg 2x" data-file-width="3000" data-file-height="2418" /></a><figcaption> <a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman</a> (erdian), EDCren sortzaileetako bat, <a href="/wiki/Los_Alamosko_Laborategi_Nazionala" title="Los Alamosko Laborategi Nazionala">Los Alamosen</a>.</figcaption></figure><p>Erradiazioa eta materiaren arteko elkarrekintza deskribatzen duen <a href="/wiki/Mekanika_kuantiko" title="Mekanika kuantiko">teoria kuantiko</a> baten lehen formulazioa <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> zientzialari britainiarrari egozten zaio, zeinak (1920ko hamarkadan) <a href="/wiki/Atomo" title="Atomo">atomo</a> baten berezko emisioaren koefizientea kalkulatu ahal izan zuen<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. </p><p>Dirac-ek <a href="/wiki/Eremu_elektromagnetiko" title="Eremu elektromagnetiko">eremu elektromagnetikoaren</a> kuantifikazioa <a href="/wiki/Osziladore_harmoniko" title="Osziladore harmoniko">oszilatzaile harmonikoen</a> multzo gisa deskribatu zuen partikulen <a href="/wiki/Sortze_eta_deuseztatze_eragileak" title="Sortze eta deuseztatze eragileak">sortze eta deuseztatze eragileen</a> kontzeptuaren sarrerarekin. Hurrengo urteetan, <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a>, <a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Eugene Wigner</a>, <a href="/w/index.php?title=Pascual_Jordan&action=edit&redlink=1" class="new" title="Pascual Jordan (sortu gabe)">Pascual Jordan</a> eta <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenbergen</a> ekarpenekin eta <a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Enrico Fermiren</a> elektrodinamika kuantikoaren formulazio dotore batekin<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>, fisikariek uste izan zuten, printzipioz, edozein konputazio egin ahal izango zela fotoi eta partikula kargatuekin. Hala ere, <a href="/wiki/Felix_Bloch" title="Felix Bloch">Felix Blochek</a> <a href="/w/index.php?title=Arnold_Nordsieck&action=edit&redlink=1" class="new" title="Arnold Nordsieck (sortu gabe)">Arnold Nordsieckekin</a><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> eta <a href="/w/index.php?title=Victor_Weisskopf&action=edit&redlink=1" class="new" title="Victor Weisskopf (sortu gabe)">Victor Weisskopfekin</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>, 1937an eta 1939an, egindako ikerketa berriek agerian utzi zuten kalkulu horiek perturbazioaren teoriaren lehen ordenan baino ez zirela fidagarriak <a href="/wiki/Robert_Oppenheimer" title="Robert Oppenheimer">Robert Oppenheimerrek</a> jada adierazitako problema batean<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>. Serieko goi ordenan, infinituak agertu ziren konputazio horiek zentzurik gabe utziz eta teoriaren beraren barne-koherentziari buruzko zalantza handiak sortuz. Garai hartan ezagutzen zen arazo horretarako konponbiderik gabe, <a href="/wiki/Erlatibitate_berezia" title="Erlatibitate berezia">erlatibitate bereziaren</a> eta <a href="/wiki/Mekanika_kuantiko" title="Mekanika kuantiko">mekanika kuantikoaren</a> arteko funtsezko bateraezintasuna zegoela zirudien. </p><p>Elektrodinamika kuantikoa <a href="/wiki/XX._mendea" title="XX. mendea">XX. mendean</a> sortu zen teoria kuantiko zehatzenetako bat da, eta hogei zifra hamartarreraino arteko kopuru fisiko jakin batzuen iragarpenak egiteko gai da, emaitza arraroa zena lehenagoko teoria fisikoetan. Hori dela eta, teoriari <i>fisikaren harribitxia</i> deitu zioten. Bere iragarpen zehatzenen artean hauek daude: </p> <ul><li><a href="/wiki/Elektroi" title="Elektroi">Elektroi</a> eta <a href="/wiki/Muoi" title="Muoi">muoien</a> momentu <a href="/wiki/Momentu_magnetiko" title="Momentu magnetiko">magnetiko</a> anomaloa, zeinarentzat Dirac-en ekuazioak balio klasikoaren balio bikoitza iragartzen zuen. Elektroiarentzat EDCk balio bat aurreikusten du:</li></ul> <blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{e}=2(1+a)=2\left(1+{\frac {q_{e}^{2}}{4\pi \epsilon _{0}hc}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>h</mi> <mi>c</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{e}=2(1+a)=2\left(1+{\frac {q_{e}^{2}}{4\pi \epsilon _{0}hc}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05a157710bd62f7c2648d1c6c576756883b4e812" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.157ex; height:6.343ex;" alt="{\displaystyle g_{e}=2(1+a)=2\left(1+{\frac {q_{e}^{2}}{4\pi \epsilon _{0}hc}}\right)}" /></span> </p> </blockquote><p>Non: </p><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{e}\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mspace width="thickmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{e}\;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51b6a8f30639bda3ae1f87954a6bdfd922b595e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.681ex; height:2.009ex;" alt="{\displaystyle q_{e}\;}" /></span> <a href="/wiki/Karga_elektriko" title="Karga elektriko">elektroiaren karga elektrikoa</a> den.</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mspace width="thickmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h\;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da77fa45168b5f31fd2e2d23bfa549dfd91307b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.984ex; height:2.176ex;" alt="{\displaystyle h\;}" /></span> <a href="/wiki/Plancken_konstantea" title="Plancken konstantea">Planck-en konstantea den</a>.</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thickmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ad932726149777ea71d4b20ea177aa1b20ba61d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.652ex; height:1.676ex;" alt="{\displaystyle c\;}" /></span> hutsean, <a href="/wiki/Argiaren_abiadura" title="Argiaren abiadura">argiaren abiadura den</a>.</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{0}\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thickmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{0}\;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abc14da2d4b1810f41daaad2488ba3cdf83ef790" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.644ex; height:2.009ex;" alt="{\displaystyle \epsilon _{0}\;}" /></span> hutsaren permitibitate elektrikoa den.</dd></dl> <ul><li>Lamb desplazamenduaren balioa <a href="/wiki/Atomo_hidrogenoide" title="Atomo hidrogenoide">hidrogeno atomoaren</a> energia-mailetan.</li></ul> <p><a href="/wiki/Sin-Itiro_Tomonaga" title="Sin-Itiro Tomonaga">Shin'ichirō Tomonaga</a>, <a href="/wiki/Julian_Schwinger" title="Julian Schwinger">Julian Schwinger</a> eta <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a>-ek <a href="/wiki/1965" title="1965">1965eko</a> <a href="/wiki/Zerrenda:Fisikako_Nobel_Saria" title="Zerrenda:Fisikako Nobel Saria">Fisikako Nobel Sariak</a> jaso zituzten beren garapenarengatik, beren ekarpenak preskripzio kobariantza eta neurgailu aldaezina kantitate behagarrien konputaziorako inplikatzen zutelarik. Feynmanen diagrametan oinarritutako teknika matematikoak, hasiera batean, Schwinger eta Tomonagako operadoreetan oinarritutako eremu teorikoaren ikuspegitik oso ezberdina zirudien, baina, geroago, bere baliokidetasuna ikusarazi zen. Eremu-teoria kuantikoaren iragarpen infinitu batzuei zentzua emateko birnormalizazio-prozedurak ere bere lehen inplementazio arrakastatsua aurkitu zuen elektrodinamika kuantikoan. </p> <div class="mw-heading mw-heading2"><h2 id="Teoriaren_deskribapena">Teoriaren deskribapena</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=2" title="Aldatu atal hau: «Teoriaren deskribapena»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=2" title="Edit section's source code: Teoriaren deskribapena"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Elektrodinamika kuantikoa <a href="/wiki/Fotoi" title="Fotoi">fotoien</a> eta <a href="/wiki/Fermioi" title="Fermioi">fermioniko</a> motako <a href="/wiki/Partikula_kargatu" title="Partikula kargatu">partikula kargatuen</a> arteko elkarrekintzaren deskribapen zehatza da. Teoria kuantikoak ezaugarri batzuk partekatzen ditu deskribapen klasikoarekin. Optika klasikoaren deskribapenaren arabera, argia baimendutako bide guztietan ibiltzen da, eta haien interferentziak <a href="/wiki/Fermaten_printzipioa" title="Fermaten printzipioa">Fermat-en printzipioaren</a> arabera hedatzen diren <a href="/wiki/Uhin_fronte" title="Uhin fronte">uhin-fronteak</a> zehazten ditu. Era berean, fotoien (eta fermioien) deskribapen kuantikoan, irekiguneek edo sistema optikoek ahalbidetzen duten bide guztietan zehar igarotzen dira. Bi kasuetan, behatzaileak lerro integraletan zehar kontuan hartutako uhin guztien gainjartzearen emaitza matematikoa besterik ez du detektatzen. Ezberdintasuna da elektrodinamikan fotoi baten abiadura eraginkorrak <a href="/wiki/Argiaren_abiadura" title="Argiaren abiadura">argiaren batez besteko abiadura</a> gaindi dezakeela<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>. </p><p>Gainera, elektrodinamika kuantikoa izan zen eremuen deskribapen osoa eraikitzeko eta partikula kuantikoen sorrera eta deuseztapenaren zailtasunak ongi ebatzi ziren lehen eremu-teoria kuantikoa. </p> <div class="mw-heading mw-heading3"><h3 id="Formalismoa">Formalismoa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=3" title="Aldatu atal hau: «Formalismoa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=3" title="Edit section's source code: Formalismoa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Feynman_Diagram_Components.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Feynman_Diagram_Components.svg/250px-Feynman_Diagram_Components.svg.png" decoding="async" width="250" height="236" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Feynman_Diagram_Components.svg/375px-Feynman_Diagram_Components.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Feynman_Diagram_Components.svg/500px-Feynman_Diagram_Components.svg.png 2x" data-file-width="760" data-file-height="718" /></a><figcaption> EDC kalkulu perturbatiboetarako erabilitako Feynmanen diagrama sinpleak.</figcaption></figure> <p>Matematikoki, elektrodinamika kuantikoak gauge-teoria <a href="/wiki/Talde_abeldar" title="Talde abeldar">abeliar</a> baten egitura duela esan dezakegu, elkartutako gauge-taldea <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathrm {U} (1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">U</mi> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathrm {U} (1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2cb5557effbccfe239ca258de8c41cd350b4c1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.334ex; height:2.176ex;" alt="{\displaystyle \scriptstyle \mathrm {U} (1)}" /></span> talde unitarioan izanik. <a href="/wiki/Spin" title="Spin">Spin</a> <a href="/wiki/Eremu_(fisika)" title="Eremu (fisika)">eremuen</a>-1/2 kargatuen arteko elkarrekintzan bitartekaritza duen gauge-eremua <a href="/wiki/Eremu_elektromagnetiko" title="Eremu elektromagnetiko">eremu elektromagnetikoa</a> da. </p><p>Kargatutako partikula eta fotoi sistema baten eboluzio tenporala kalkulu perturbatibo baten bidez kalkula daiteke. Zehazki, maiz egin daitezkeen esperimentuekin alderatzeko, <b>S</b> matrizeko elementuak kalkulatzea eskatzen du, zeinak esperimentuen emaitzekin alderatu daitezkeen partikularen dispertsioaren ebakidurak aurkitzea ahalbidetzen duten. </p><p>Elektrodinamika kuantikoak kalkulu mota hori <a href="/wiki/Berretura-serie" title="Berretura-serie">potentzia-serieko</a> garapen perturbatibo batera murrizten du, sekzio eraginkor horiek nahi den zehaztasunarekin aurkitzea ahalbidetzen duena. Termino perturbatibo bakoitzak <a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynmanen</a> diagrama izenez ezagutzen den irudikapen grafiko bat onartzen du. Izan ere, historikoki, elektrodinamika kuantikoa izan zen lehen teoria, non Feynmanen diagramak kalkulu perturbatiboa laguntzeko erabili zen. Termino perturbatibo bakoitzaren forma eta, beraz, erlazionatutako irudikapen grafikoa teoria hori ezaugarritzen duen <a href="/wiki/Lagrangear_mekanika" class="mw-redirect" title="Lagrangear mekanika">lagrangiarren</a> formaren araberakoa da. </p> <div class="mw-heading mw-heading3"><h3 id="Tokiko_'"`UNIQ--postMath-00000007-QINU`"'_neurgailuaren_aldaezintasuna"><span id="Tokiko_.7F.27.22.60UNIQ--postMath-00000007-QINU.60.22.27.7F_neurgailuaren_aldaezintasuna"></span>Tokiko <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {U} (1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">U</mi> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {U} (1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e002937bc66667b3508046146eb651b4ffe68b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.715ex; height:2.843ex;" alt="{\displaystyle \mathrm {U} (1)}" /></span> neurgailuaren aldaezintasuna</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=4" title="Aldatu atal hau: «Tokiko '"`UNIQ--postMath-00000007-QINU`"' neurgailuaren aldaezintasuna»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=4" title="Edit section's source code: Tokiko '"`UNIQ--postMath-00000007-QINU`"' neurgailuaren aldaezintasuna"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Interesgarria da ikustea nola aurki daitekeen EDCren lagrangiarra baldintza soila izanik <a href="/wiki/Karga_elektriko" title="Karga elektriko">karga elektriko</a> ez nulua duen <a href="/wiki/Fermioi" title="Fermioi">fermioi</a> aske baten lagrangiarra tokiko gauge aldaezina izanda. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1642de4c4f97533bc5de617a588564047b1c4577" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.326ex; height:2.509ex;" alt="{\displaystyle {\mathcal {L}}_{l}}" /></span> fermioi askearen lagrangiarra den:</p><blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}_{l}={\dot {\imath }}{\bar {\psi }}\gamma ^{\mu }\partial _{\mu }\psi -m{\bar {\psi }}\psi ={\bar {\psi }}({\dot {\imath }}\gamma ^{\mu }\partial _{\mu }-m)\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ı</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mi>ψ</mi> <mo>−</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mi>ψ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ı</mi> <mo>˙</mo> </mover> </mrow> </mrow> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>−</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}_{l}={\dot {\imath }}{\bar {\psi }}\gamma ^{\mu }\partial _{\mu }\psi -m{\bar {\psi }}\psi ={\bar {\psi }}({\dot {\imath }}\gamma ^{\mu }\partial _{\mu }-m)\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c449c332039b31252e8542f37876bdf8104b31e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:41.77ex; height:3.176ex;" alt="{\displaystyle {\mathcal {L}}_{l}={\dot {\imath }}{\bar {\psi }}\gamma ^{\mu }\partial _{\mu }\psi -m{\bar {\psi }}\psi ={\bar {\psi }}({\dot {\imath }}\gamma ^{\mu }\partial _{\mu }-m)\psi }" /></span> </p> </blockquote><p>Beste era batera esanda, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {U} (1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">U</mi> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {U} (1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e002937bc66667b3508046146eb651b4ffe68b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.715ex; height:2.843ex;" alt="{\displaystyle \mathrm {U} (1)}" /></span> tokiko transformazio baten behean <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1642de4c4f97533bc5de617a588564047b1c4577" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.326ex; height:2.509ex;" alt="{\displaystyle {\mathcal {L}}_{l}}" /></span> aldaezina izan dadin nahi dugu; beraz, eremua honela aldatzen da:</p><blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi (x)\rightarrow e^{-{\dot {\imath }}\alpha (x)}\psi (x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ı</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mi>α</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (x)\rightarrow e^{-{\dot {\imath }}\alpha (x)}\psi (x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d21f0401cef5e138f7c11daafb1cef51a3b4d69e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.642ex; height:3.509ex;" alt="{\displaystyle \psi (x)\rightarrow e^{-{\dot {\imath }}\alpha (x)}\psi (x)}" /></span> </p> </blockquote><p>Kasu horretan, <a href="/wiki/Deribatu_kobariante" title="Deribatu kobariante">deribatu kobariantza</a> eta neurgailua honako hauek izango dira:</p><blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{\mu }=\partial _{\mu }-{\dot {\imath }}eA_{\mu }\qquad \therefore \qquad A_{\mu }\rightarrow A_{\mu }-{\frac {1}{e}}\partial _{\mu }\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ı</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mi>e</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mspace width="2em"></mspace> <mo>∴</mo> <mspace width="2em"></mspace> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>e</mi> </mfrac> </mrow> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{\mu }=\partial _{\mu }-{\dot {\imath }}eA_{\mu }\qquad \therefore \qquad A_{\mu }\rightarrow A_{\mu }-{\frac {1}{e}}\partial _{\mu }\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d37a51ac3d186480d13d4597efc91e1e46486b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:47.271ex; height:5.176ex;" alt="{\displaystyle D_{\mu }=\partial _{\mu }-{\dot {\imath }}eA_{\mu }\qquad \therefore \qquad A_{\mu }\rightarrow A_{\mu }-{\frac {1}{e}}\partial _{\mu }\alpha }" /></span> </p> </blockquote><p>Horrekin guztiarekin, elektrodinamika kuantikoaren lagrangiarra honela geratzen da:</p><blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}_{QED}={\bar {\psi }}\left({\dot {\imath }}\gamma ^{\mu }\partial _{\mu }-m\right)\psi +e{\bar {\psi }}\gamma ^{\mu }A_{\mu }\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> <mi>E</mi> <mi>D</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ı</mi> <mo>˙</mo> </mover> </mrow> </mrow> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>−</mo> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo>+</mo> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mi>ψ</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}_{QED}={\bar {\psi }}\left({\dot {\imath }}\gamma ^{\mu }\partial _{\mu }-m\right)\psi +e{\bar {\psi }}\gamma ^{\mu }A_{\mu }\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a00c08badac5ad3953f6c33c4ea99fe8140c03f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:50.439ex; height:5.176ex;" alt="{\displaystyle {\mathcal {L}}_{QED}={\bar {\psi }}\left({\dot {\imath }}\gamma ^{\mu }\partial _{\mu }-m\right)\psi +e{\bar {\psi }}\gamma ^{\mu }A_{\mu }\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }}" /></span> </p> </blockquote> <div class="mw-heading mw-heading3"><h3 id="Egokitasun_esperimentala">Egokitasun esperimentala</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=5" title="Aldatu atal hau: «Egokitasun esperimentala»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=5" title="Edit section's source code: Egokitasun esperimentala"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kontuan izan behar da elektrodinamika kuantikoak ez duela esperimentu zehatz batean gertatuko litzatekeenaren balio zehatzik ematen; egoera mota jakin bat gertatzeko probabilitateak soilik ematen ditu. Horregatik, teoriak aurreikusitako probabilitateen arabera, estatistikoki sakabanatuta dauden partikula kopuru handi samarra erabiltzen dute esperimentuek. Sakabanatuta dauden partikulen banaketatik, ebakidura neur daiteke teoriaren zenbakizko iragarpenekin alderatuta. </p><p>Elektrodinamika kuantikoaren iragarpenak ezohiko zehaztasun maila batera baieztatu dituzte esperimentuek: normalean, teoriaren iragarpenekin 12 zifra hamartar zuzenekin bat egiten duten esperimentuak izaten dira. Horrek gizakiak eraikitako teoriarik zehatzena bihurtzen du EDC kuantikoa. </p> <div class="mw-heading mw-heading2"><h2 id="Formulazio_matematikoa">Formulazio matematikoa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=6" title="Aldatu atal hau: «Formulazio matematikoa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=6" title="Edit section's source code: Formulazio matematikoa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Eremu-teoria baten oinarrizko dinamika eta propietateak lagrangiarretzat aukeratutako formaren araberakoak dira. Lagrangiarren hautaketa gauge-taldearen simetrien araberakoa da, eta teoriak fermioi kargatuen arteko elkarrekintza egoki deskribatzen duenaren araberakoa da. Eremu fermionikoak gauge-talde kommutatiboa den masarik gabeko partikulei (fotoiei) lotutako eremu bosoiko baten bidez elkarreraginean deskribatzen duen teorian, hasierako lagrangiarra honela har daiteke:</p><blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <p><span style="float:right; width:10%; text-align:right;">(<cite id="Equation_1" style="font-style: normal;"><a href="#Eqnref_1">1</a></cite>)</span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}=i{\bar {\psi }}\gamma ^{\mu }\partial _{\mu }\psi -e{\bar {\psi }}\gamma _{\mu }A^{\mu }\psi -m{\bar {\psi }}\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mo>=</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mi>ψ</mi> <mo>−</mo> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msub> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mi>ψ</mi> <mo>−</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mi>ψ</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}=i{\bar {\psi }}\gamma ^{\mu }\partial _{\mu }\psi -e{\bar {\psi }}\gamma _{\mu }A^{\mu }\psi -m{\bar {\psi }}\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2c2dbd81ddf2bbfa6fcddd950476b124d06bb7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:46.716ex; height:5.176ex;" alt="{\displaystyle {\mathcal {L}}=i{\bar {\psi }}\gamma ^{\mu }\partial _{\mu }\psi -e{\bar {\psi }}\gamma _{\mu }A^{\mu }\psi -m{\bar {\psi }}\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }\,}" /></span> </p> </blockquote><p>non eremu ferminikoa<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/133059010c33954db6f4c65aa66e9960807f4e2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.094ex; height:2.509ex;" alt="{\displaystyle \ \psi }" /></span> eta bere <a href="/wiki/Paul_Dirac" title="Paul Dirac">ordezko de Dirac</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {\psi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {\psi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/890adebe2730294079a81b7bf08b2fe0f2c59909" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.596ex; height:2.843ex;" alt="{\displaystyle {\bar {\psi }}}" /></span> elektrikoki kargatutako partikulak adierazten dituzten eremuak diren, zehazki, <a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac-en spinor</a> gisa irudikatzen diren <a href="/wiki/Elektroi" title="Elektroi">elektroi</a> eta <a href="/wiki/Positroi" title="Positroi">positroi</a> eremuak. Eremu elektromagnetikoko tentsorea duen lagrangiar zatiak eremu <a href="/wiki/Eremu_elektromagnetiko" title="Eremu elektromagnetiko">elektromagnetikoaren</a> bilakaera askea deskribatzen du; bien bitartean, gauge-ren <a href="/wiki/Deribatu" title="Deribatu">deribatu</a> kobariantzarekin, <a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac ekuazioak</a> <a href="/wiki/Elektroi" title="Elektroi">elektroi</a> eta <a href="/wiki/Positroi" title="Positroi">positroi</a> eremuen bilakaera askea eta eremuarekin duten elkarrekintza deskribatzen du. </p><div class="mw-heading mw-heading3"><h3 id="Higidura-ekuazioak">Higidura-ekuazioak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=7" title="Aldatu atal hau: «Higidura-ekuazioak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=7" title="Edit section's source code: Higidura-ekuazioak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Higidura</i> edo Mugimenduaren ekuazioak elektrodinamika kuantikoaren edo denboraren bilakaeraren ekuazioak lor daitezke Euler-Lagrange ekuazioaren teoriaren lagrangiarretik. Lagrangiar hori Euler-Lagrange ekuazioetan txertatuz, teoriaren denbora-eboluzioaren ekuazioa lortzen da:</p><blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <p><span style="float:right; width:10%; text-align:right;">(<cite id="Equation_2" style="font-style: normal;"><a href="#Eqnref_2">2</a></cite>)</span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial _{\mu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\mu }\psi )}}\right)-{\frac {\partial {\mathcal {L}}}{\partial \psi }}=0\quad {\mbox{con}}{\begin{cases}\partial _{\mu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\mu }\psi )}}\right)=\partial _{\mu }\left(i{\bar {\psi }}\gamma ^{\mu }\right)\\{\frac {\partial {\mathcal {L}}}{\partial \psi }}=-e{\bar {\psi }}\gamma _{\mu }A^{\mu }-m{\bar {\psi }}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mi>ψ</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ψ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="1em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>con</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mi>ψ</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ψ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msub> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mo>−</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\mu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\mu }\psi )}}\right)-{\frac {\partial {\mathcal {L}}}{\partial \psi }}=0\quad {\mbox{con}}{\begin{cases}\partial _{\mu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\mu }\psi )}}\right)=\partial _{\mu }\left(i{\bar {\psi }}\gamma ^{\mu }\right)\\{\frac {\partial {\mathcal {L}}}{\partial \psi }}=-e{\bar {\psi }}\gamma _{\mu }A^{\mu }-m{\bar {\psi }}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87194c1c72b5cd60f4678423d07caca7fc7919fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.624ex; margin-bottom: -0.214ex; width:58.242ex; height:8.843ex;" alt="{\displaystyle \partial _{\mu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\mu }\psi )}}\right)-{\frac {\partial {\mathcal {L}}}{\partial \psi }}=0\quad {\mbox{con}}{\begin{cases}\partial _{\mu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\mu }\psi )}}\right)=\partial _{\mu }\left(i{\bar {\psi }}\gamma ^{\mu }\right)\\{\frac {\partial {\mathcal {L}}}{\partial \psi }}=-e{\bar {\psi }}\gamma _{\mu }A^{\mu }-m{\bar {\psi }}\end{cases}}}" /></span> </p> </blockquote><p>Bi terminoak Euler-Lagrange ekuazioaren barruan kokatuz gero, azkenik, eremu fermionikoaren bilakaera-ekuazio hau lortzen da: </p><p>Ezkerreko kidea Dirac-en ekuazioa da, eta eskuineko terminoak <a href="/wiki/Eremu_elektromagnetiko" title="Eremu elektromagnetiko">eremu elektromagnetikoarekiko</a> elkarrekintza adierazten du. </p><p> Euler-Lagrange ekuazio berak, orain <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A^{\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1da55ba40017c25d210f7e269efb2d6d539a1b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.967ex; height:2.343ex;" alt="{\displaystyle A^{\mu }}" /></span> eremuari aplikatuta, eremu elektromagnetikoaren bilakaera-ekuazioak aurkitzea ahalbidetzen du:</p><blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <p><span style="float:right; width:10%; text-align:right;">(<cite id="Equation_3" style="font-style: normal;"><a href="#Eqnref_3">3</a></cite>)</span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial _{\nu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\nu }A_{\mu })}}\right)-{\frac {\partial {\mathcal {L}}}{\partial A_{\mu }}}=0\quad {\mbox{con}}{\begin{cases}\partial _{\nu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\nu }A_{\mu })}}\right)=\partial _{\nu }\left(\partial ^{\mu }A^{\nu }-\partial ^{\nu }A^{\mu }\right)\\{\frac {\partial {\mathcal {L}}}{\partial A_{\mu }}}=-e{\bar {\psi }}\gamma ^{\mu }\psi \end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="1em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>con</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <mo>−</mo> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mi>ψ</mi> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\nu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\nu }A_{\mu })}}\right)-{\frac {\partial {\mathcal {L}}}{\partial A_{\mu }}}=0\quad {\mbox{con}}{\begin{cases}\partial _{\nu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\nu }A_{\mu })}}\right)=\partial _{\nu }\left(\partial ^{\mu }A^{\nu }-\partial ^{\nu }A^{\mu }\right)\\{\frac {\partial {\mathcal {L}}}{\partial A_{\mu }}}=-e{\bar {\psi }}\gamma ^{\mu }\psi \end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/652ca6d92441ffd4eadecd21c46797efe11746de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:70.057ex; height:9.176ex;" alt="{\displaystyle \partial _{\nu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\nu }A_{\mu })}}\right)-{\frac {\partial {\mathcal {L}}}{\partial A_{\mu }}}=0\quad {\mbox{con}}{\begin{cases}\partial _{\nu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\nu }A_{\mu })}}\right)=\partial _{\nu }\left(\partial ^{\mu }A^{\nu }-\partial ^{\nu }A^{\mu }\right)\\{\frac {\partial {\mathcal {L}}}{\partial A_{\mu }}}=-e{\bar {\psi }}\gamma ^{\mu }\psi \end{cases}}}" /></span> </p> </blockquote><p>Eta, azkenik, eremu elektromagnetikoaren bilakaeraren ekuazioa hau da: </p><dl><dd><dl><dd><table cellpadding="2" style="border:2px solid #ccccff"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial _{\nu }F^{\nu \mu }=e{\bar {\psi }}\gamma ^{\mu }\psi \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mi>μ</mi> </mrow> </msup> <mo>=</mo> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mi>ψ</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\nu }F^{\nu \mu }=e{\bar {\psi }}\gamma ^{\mu }\psi \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c35eac2fe30f90017332dd61e1d680bed547304e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.428ex; height:3.009ex;" alt="{\displaystyle \partial _{\nu }F^{\nu \mu }=e{\bar {\psi }}\gamma ^{\mu }\psi \,}" /></span> </td></tr></tbody></table></dd></dl></dd></dl> <p>non bigarren kidea eremu fermionikoari lotutako korronte-dentsitate bezala interpreta daitekeen. </p> <div class="mw-heading mw-heading3"><h3 id="Feynmanen_arauak">Feynmanen arauak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=8" title="Aldatu atal hau: «Feynmanen arauak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=8" title="Edit section's source code: Feynmanen arauak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Efektu kuantiko guztiak kontuan hartzeko, beharrezkoa da aurreko ekuazio diferentzialetako eremu-osagaiak ordeztea benetako operadore kuantiko gisa interpreta daitezkeen operadore autoadjuntuez. Oro har, horrek zehatz-mehatz integratzen ez dakigun baina tratamendu perturbatiboa onartzen duten ekuazio-sistemak ekartzen ditu denbora-eboluzio-operadorea deskonposatuz <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {U}}_{QED}=\exp(it{\hat {H}}_{QED})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>U</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> <mi>E</mi> <mi>D</mi> </mrow> </msub> <mo>=</mo> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>i</mi> <mi>t</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> <mi>E</mi> <mi>D</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {U}}_{QED}=\exp(it{\hat {H}}_{QED})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d7249c2910dfc1980c5c2a7ecd6ceba397b70d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.245ex; height:3.509ex;" alt="{\displaystyle {\hat {U}}_{QED}=\exp(it{\hat {H}}_{QED})}" /></span> potentzia-seriean edo serie perturbatiboan. </p><p>Aurreko serieko termino bakoitzaren kalkulua ia automatikoki egin daiteke Feynmanen diagrama deritzonen laguntzaz, zeinari Feynmanen arau batzuk lotu ahal zaizkien. Kalkuluaren zehaztasuna aurreko serie perturbatiboetan zenbat termino kontuan hartzen diren araberakoa da. </p> <div class="mw-heading mw-heading3"><h3 id="Birnormalizazioa">Birnormalizazioa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=9" title="Aldatu atal hau: «Birnormalizazioa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=9" title="Edit section's source code: Birnormalizazioa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Feynmanen arauen arazo larri bat da, lehen aldian adierazi zuten bezala, serie perturbatiboko diagrama eta termino dibergenteetara daramatzatela, hau da, termino ez finituen kalkulua termino finituen kalkulua alferrik galarazten dutela. Jakina, emaitza fisiko guztiak finituak dira, eta kalkuluaren termino dibergente horiek, errealitatean, ez dira behagarriak. Birnormalizazioa, kalkulatutako terminoen eta termino neurgarrien artean errealitatean zer erlazio dagoen interpretatzen duten arau gehigarrien multzoa da, eta kalkuluak <i>normalizatzea</i> ahalbidetzen duten arau osagarriak sortzen dituzte, eta errealitatearekin alderagarriak diren zenbakizko emaitza finituak esperimentu bidez sortzen direla ziurtatzen dute. </p><p>Jakina da teoria kuantikoa gauge-eremuaren teoria izateak normalizagarria izateko propietatea ematen diola, hau da, arau gehigarri bat dagoela behatu ezin diren termino dibergenteak ezabatzea ahalbidetzen duena eta emaitza finituak sorrarazten dituena. </p> <div class="mw-heading mw-heading2"><h2 id="Erreferentziak">Erreferentziak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=10" title="Aldatu atal hau: «Erreferentziak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=10" title="Edit section's source code: Erreferentziak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">↑</a> <span class="reference-text"><a href="https://en.wikipedia.org/wiki/Richard_Feynman" class="extiw" title="en:Richard Feynman">Feynman, Richard</a> (1985). <i>QED: The Strange Theory of Light and Matter</i>. Princeton University Press. <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-691-12575-6" class="extiw" title="en:Special:BookSources/978-0-691-12575-6">ISBN <bdi>978-0-691-12575-6</bdi>.</a></span> </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> <span class="reference-text"><span class="citation"> <span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Ingelesez dago aipu honen iturburua"><b>(Ingelesez)</b></span></span> <span class="citation"><a rel="nofollow" class="external text" href="https://royalsocietypublishing.org/doi/10.1098/rspa.1927.0039">«The quantum theory of the emission and absorption of radiation»</a> <i>Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character</i> 114 (767): 243–265. 1927-03  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098%2Frspa.1927.0039">10.1098/rspa.1927.0039</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0950-1207">0950-1207</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-02-16)</small></span></span>.</span> </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> <span class="reference-text"><span class="citation"> <span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Ingelesez dago aipu honen iturburua"><b>(Ingelesez)</b></span></span> <span class="citation"> <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Reviews_of_Modern_Physics&oldid=1092592970"><i>Reviews of Modern Physics. </i></a> 2022-06-11 <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-02-16)</small></span></span>.</span> </li> <li id="cite_note-4"><a href="#cite_ref-4">↑</a> <span class="reference-text"><a href="https://en.wikipedia.org/wiki/Felix_Bloch" class="extiw" title="en:Felix Bloch">Bloch, F</a>.; <a href="https://en.wikipedia.org/wiki/Arnold_Nordsieck" class="extiw" title="en:Arnold Nordsieck">Nordsieck, A.</a> (1937). "Note on the Radiation Field of the Electron". <i><a href="https://en.wikipedia.org/wiki/Physical_Review" class="extiw" title="en:Physical Review">Physical Review</a></i>. <b>52</b> (2): 54–59. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1937PhRv...52...54B">Bibcode:1937PhRv...52...54B</a>. <a href="//doi.org/10.1103/PhysRev.52.54" class="extiw" title="doi:10.1103/PhysRev.52.54">doi:10.1103/PhysRev.52.54</a>.</span> </li> <li id="cite_note-5"><a href="#cite_ref-5">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFWeisskopf1939-07-01">Weisskopf, V. F..  (1939-07-01). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRev.56.72">«On the Self-Energy and the Electromagnetic Field of the Electron»</a> <i>Physical Review</i> 56 (1): 72–85.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.56.72">10.1103/PhysRev.56.72</a></span>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-02-16)</small></span></span>.</span> </li> <li id="cite_note-6"><a href="#cite_ref-6">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFOppenheimer1930-03-01">Oppenheimer, J. R..  (1930-03-01). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRev.35.461">«Note on the Theory of the Interaction of Field and Matter»</a> <i>Physical Review</i> 35 (5): 461–477.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.35.461">10.1103/PhysRev.35.461</a></span>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-02-16)</small></span></span>.</span> </li> <li id="cite_note-7"><a href="#cite_ref-7">↑</a> <span class="reference-text">Richard P. Feynman QED:(<a href="/w/index.php?title=QED_(book)&action=edit&redlink=1" class="new" title="QED (book) (sortu gabe)">QED (book)</a>) p89-90 "the light has an amplitude to go faster or slower than the speed <i>c</i>, but these amplitudes cancel each other out over long distances"; see also accompanying text</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=11" title="Aldatu atal hau: «Bibliografia»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=11" title="Edit section's source code: Bibliografia"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Liburuak">Liburuak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=12" title="Aldatu atal hau: «Liburuak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=12" title="Edit section's source code: Liburuak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>De Broglie, Louis (1925). Recherches sur la theorie des quanta [Research on quantum theory]. France: Wiley-Interscience. </li> <li>Feynman, Richard Phillips (1998). Quantum Electrodynamics (New edición). Westview Press. <a href="/wiki/Berezi:BookSources/9780201360752" class="internal mw-magiclink-isbn">ISBN 978-0-201-36075-2</a>. </li> <li>Jauch, J.M.; Rohrlich, F. (1980). The Theory of Photons and Electrons. Springer-Verlag. <a href="/wiki/Berezi:BookSources/9780387072951" class="internal mw-magiclink-isbn">ISBN 978-0-387-07295-1</a>. (requiere registro). </li> <li>Greiner, Walter; Bromley, D.A.; Müller, Berndt (2000). Gauge Theory of Weak Interactions. Springer. <a href="/wiki/Berezi:BookSources/9783540676720" class="internal mw-magiclink-isbn">ISBN 978-3-540-67672-0</a>. </li> <li>Kane, Gordon, L. (1993). Modern Elementary Particle Physics. Westview Press. <a href="/wiki/Berezi:BookSources/9780201624601" class="internal mw-magiclink-isbn">ISBN 978-0-201-62460-1</a>. </li> <li>Miller, Arthur I. (1995). Early Quantum Electrodynamics: A Sourcebook. Cambridge University Press. <a href="/wiki/Berezi:BookSources/9780521568913" class="internal mw-magiclink-isbn">ISBN 978-0-521-56891-3</a>. </li> <li>Milonni, Peter W. (1994). The Quantum Vacuum: An Introduction to Quantum Electrodynamics. Boston: Academic Press. <a href="/wiki/Berezi:BookSources/0124980805" class="internal mw-magiclink-isbn">ISBN 0124980805</a>. LCCN 93029780. OCLC 422797902. </li> <li>Schweber, Silvan S. (1994). QED and the Men Who Made It. Princeton University Press. <a href="/wiki/Berezi:BookSources/9780691033273" class="internal mw-magiclink-isbn">ISBN 978-0-691-03327-3</a>. (requiere registro). </li> <li>Schwinger, Julian (1958). Selected Papers on Quantum Electrodynamics. Dover Publications. <a href="/wiki/Berezi:BookSources/9780486604442" class="internal mw-magiclink-isbn">ISBN 978-0-486-60444-2</a>. </li> <li>Tannoudji-Cohen, Claude; Dupont-Roc, Jacques; Grynberg, Gilbert (1997). Photons and Atoms: Introduction to Quantum Electrodynamics. Wiley-Interscience. <a href="/wiki/Berezi:BookSources/9780471184331" class="internal mw-magiclink-isbn">ISBN 978-0-471-18433-1</a>. </li></ul> <div class="mw-heading mw-heading3"><h3 id="Aldizkariak">Aldizkariak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=13" title="Aldatu atal hau: «Aldizkariak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=13" title="Edit section's source code: Aldizkariak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation"></span> <span class="citation" id="CITEREFDudleyKwan1996">Dudley, J.M.; Kwan, A.M..  (1996). «Richard Feynman's popular lectures on quantum electrodynamics: The 1979 Robb Lectures at Auckland University» <i>American Journal of Physics</i> 64 (6): 694–98.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1119%2F1.18234">10.1119/1.18234</a></span>. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1996AmJPh..64..694D">1996AmJPh..64..694D</a>.</span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Kanpo_estekak">Kanpo estekak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrodinamika_kuantiko&veaction=edit&section=14" title="Aldatu atal hau: «Kanpo estekak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrodinamika_kuantiko&action=edit&section=14" title="Edit section's source code: Kanpo estekak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="clear:both;"></div><style data-mw-deduplicate="TemplateStyles:r7786466">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control,.mw-parser-output .mw-mf-linked-projects{border:1px solid #a2a9b1;font-size:88%}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}</style><div class="mw-authority-control"><div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r9236167">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid 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