Farbladung – Wikipedia

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property="og:image:height" content="610"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Farbladung – Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//de.m.wikipedia.org/wiki/Farbladung"> <link rel="alternate" type="application/x-wiki" title="Seite bearbeiten" href="/w/index.php?title=Farbladung&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (de)"> <link rel="EditURI" type="application/rsd+xml" href="//de.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://de.wikipedia.org/wiki/Farbladung"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.de"> <link rel="alternate" type="application/atom+xml" title="Atom-Feed für „Wikipedia“" href="/w/index.php?title=Spezial:Letzte_%C3%84nderungen&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin-vector-legacy mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Farbladung rootpage-Farbladung skin-vector action-view"><div id="mw-page-base" class="noprint"></div> <div id="mw-head-base" class="noprint"></div> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice"></div> <div class="mw-indicators"> </div> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Farbladung</span></h1> <div id="bodyContent" class="vector-body"> <div id="siteSub" class="noprint">aus Wikipedia, der freien Enzyklopädie</div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="contentSub2"></div> <div id="jump-to-nav"></div> <a class="mw-jump-link" href="#mw-head">Zur Navigation springen</a> <a class="mw-jump-link" href="#searchInput">Zur Suche springen</a> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Datei:Synthese%2B.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Synthese%2B.svg/220px-Synthese%2B.svg.png" decoding="async" width="220" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Synthese%2B.svg/330px-Synthese%2B.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Synthese%2B.svg/440px-Synthese%2B.svg.png 2x" data-file-width="512" data-file-height="488" /></a><figcaption>Konzeptfarben für die Farbladung: rot, grün, blau / cyan, magenta, gelb</figcaption></figure> <p>Die <b>Farbladung</b>, kurz auch <b>Farbe</b>, eines <a href="/wiki/Teilchen_(Physik)" class="mw-redirect" title="Teilchen (Physik)">Teilchens</a> ist in der <a href="/wiki/Elementarteilchenphysik" class="mw-redirect" title="Elementarteilchenphysik">Elementarteilchenphysik</a> eine Größe, die in der <a href="/wiki/Quantenchromodynamik" title="Quantenchromodynamik">Quantenchromodynamik</a> beschreibt, wie sich das Teilchen unter der <a href="/wiki/Starke_Wechselwirkung" title="Starke Wechselwirkung">starken Wechselwirkung</a> verhält. Alle stark wechselwirkenden Teilchen haben Farbe; diese sind im <a href="/wiki/Standardmodell" title="Standardmodell">Standardmodell</a> der Teilchenphysik die <a href="/wiki/Quark_(Physik)" title="Quark (Physik)">Quarks</a> und die <a href="/wiki/Gluon" title="Gluon">Gluonen</a>. Alle anderen Elementarteilchen sind farblos. Physikalisch gesprochen befinden sich die Quarks und Gluonen in einer nichttrivialen <a href="/wiki/Darstellung_(Gruppe)" title="Darstellung (Gruppe)">Darstellung</a> der <a href="/wiki/Symmetrie_(Physik)" title="Symmetrie (Physik)">Symmetriegruppe</a> der Quantenchromodynamik, die anderen Elementarteilchen in der trivialen. Das Konzept wurde 1964 von <a href="/wiki/Oscar_Wallace_Greenberg" title="Oscar Wallace Greenberg">Oscar Wallace Greenberg</a><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> sowie unabhängig davon 1965 von <a href="/wiki/Moo-Young_Han" title="Moo-Young Han">Moo-Young Han</a> und <a href="/wiki/Yoichiro_Nambu" class="mw-redirect" title="Yoichiro Nambu">Yoichiro Nambu</a><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> vorgeschlagen. </p><p>Die Bezeichnung als Farbe ist ebenso irreführend wie die Bezeichnung als Ladung: Weder entspricht die Farbe der Quantenchromodynamik der optischen <a href="/wiki/Farbe" title="Farbe">Farbe</a> eines makroskopischen Objekts, noch ist die Farbladung die <a href="/wiki/Ladung_(Physik)" title="Ladung (Physik)">Ladung</a> der starken Wechselwirkung. Stattdessen kann Farbe am ehesten in Analogie zum <a href="/wiki/Spin" title="Spin">Spin</a> eines Teilchens aufgefasst werden, bei dem ein klassisches Teilchen in der Quantenmechanik als zweikomponentige <a href="/wiki/Wellenfunktion" title="Wellenfunktion">Wellenfunktion</a> dargestellt wird: In der Beschreibung durch die Quantenchromodynamik hat die Wellenfunktion eines Quarks drei Komponenten, die mit den drei Grundfarben rot, grün und blau bezeichnet werden, die Farben eines <a href="/wiki/Antimaterie" title="Antimaterie">Antiquarks</a> entsprechen den drei Antifarben (Sekundärfarben) antirot (cyan), antigrün (magenta) und antiblau (gelb). Gluonen bestehen aus einer Kombination von Farben und Antifarben und werden durch Matrizen im Farbraum beschrieben. </p><p>Zu der Bezeichnung dieser Eigenschaft als „Farbe“ schreibt der Physik-Nobelpreisträger <a href="/wiki/Richard_P._Feynman" class="mw-redirect" title="Richard P. Feynman">Richard P. Feynman</a>: </p> <div class="Vorlage_Zitat" style="margin:1em 40px;"> <div style="margin:1em 0;"><blockquote style="margin:0;"> <p>„The idiot physicists, unable to come up with any wonderful Greek words anymore, call this type of polarization by the unfortunate name of ‚color,‘ [sic!] which has nothing to do with the color in the normal sense.“ </p> </blockquote> <blockquote style="margin:.5em 0 0 0;" lang="de-Latn"> <p>„Diese Physiker-Idioten, unfähig sich irgendwelche wundervollen griechischen Wörter auszudenken, bezeichnen diese Art der Polarisation mit dem unglücklichen Begriff ‚Farbe,‘ [sic!] der nichts mit der Farbe im üblichen Sinn zu tun hat.“ </p> </blockquote></div><div class="cite" style="margin:-1em 0 1em 1em;">– <style data-mw-deduplicate="TemplateStyles:r181095833">.mw-parser-output .Person{font-variant:small-caps}</style><span class="Person h-card">Richard P. Feynman</span>: <cite style="font-style:normal">QED: The Strange Theory of Light and Matter</cite><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></div></div> <p>Die Analogie zwischen optischer Farbe und quantenchromodynamischer Farbe ist folgende: Ebenso wie sich die drei optischen Grundfarben zu weiß <a href="/wiki/Additive_Farbmischung" title="Additive Farbmischung">addieren</a>, besitzt ein Objekt, das aus Farbe und zugehöriger Antifarbe, aus drei Farben oder aus drei Antifarben zusammengesetzt ist, keine starke Ladung. </p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="de" dir="ltr"><h2 id="mw-toc-heading">Inhaltsverzeichnis</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Historischer_Hintergrund"><span class="tocnumber">1</span> <span class="toctext">Historischer Hintergrund</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#Mathematische_Beschreibung"><span class="tocnumber">2</span> <span class="toctext">Mathematische Beschreibung</span></a> <ul> <li class="toclevel-2 tocsection-3"><a href="#Beschreibung_der_Gluonen"><span class="tocnumber">2.1</span> <span class="toctext">Beschreibung der Gluonen</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-4"><a href="#Singuletts_und_Confinement"><span class="tocnumber">3</span> <span class="toctext">Singuletts und Confinement</span></a></li> <li class="toclevel-1 tocsection-5"><a href="#Weblinks"><span class="tocnumber">4</span> <span class="toctext">Weblinks</span></a></li> <li class="toclevel-1 tocsection-6"><a href="#Literatur"><span class="tocnumber">5</span> <span class="toctext">Literatur</span></a></li> <li class="toclevel-1 tocsection-7"><a href="#Einzelnachweise"><span class="tocnumber">6</span> <span class="toctext">Einzelnachweise</span></a></li> </ul> </div> <div class="mw-heading mw-heading2"><h2 id="Historischer_Hintergrund">Historischer Hintergrund</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Farbladung&veaction=edit&section=1" title="Abschnitt bearbeiten: Historischer Hintergrund" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Farbladung&action=edit&section=1" title="Quellcode des Abschnitts bearbeiten: Historischer Hintergrund"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Im Jahr 1951 wurde das <a href="/wiki/%CE%94-Baryon" title="Δ-Baryon"><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 \Delta ^{++}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> <mo>+</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta ^{++}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91dec9934f3e4b9ccdbc81363385e34fbbb6f1ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.725ex; height:2.509ex;" alt="{\displaystyle \Delta ^{++}}"></span>-Baryon</a> entdeckt. Es besteht aus drei identischen u-Quarks, die keinen <a href="/wiki/Bahndrehimpuls" class="mw-redirect" title="Bahndrehimpuls">Bahndrehimpuls</a> besitzen, sodass das Baryon räumlich symmetrisch ist und eine symmetrische Spinwellenfunktion mit Gesamt<a href="/wiki/Spin" title="Spin">spin</a> 3/2 hat. Als Baryon ist das Teilchen jedoch ein <a href="/wiki/Fermion" title="Fermion">Fermion</a> und muss daher eine <a href="/wiki/Antisymmetrische_Funktion" title="Antisymmetrische Funktion">antisymmetrische</a> Gesamtwellenfunktion aufweisen. Daher war es naheliegend, einen zusätzlichen diskreten <a href="/wiki/Freiheitsgrad" title="Freiheitsgrad">Freiheitsgrad</a> einzuführen. Damit dieser zusätzliche Freiheitsgrad bei drei Quarks zu einem antisymmetrischen Zustand führen kann, muss dieser mindestens drei verschiedene Werte annehmen können. </p><p>Ein weiterer Hinweis auf verborgene Freiheitsgrade der Quarks kam aus der Messung von <a href="/wiki/Streuquerschnitt" class="mw-redirect" title="Streuquerschnitt">Streuquerschnitten</a> an Elektron-<a href="/wiki/Positron" title="Positron">Positron</a>-<a href="/wiki/Collider" class="mw-redirect" title="Collider">Collidern</a>. Beim Vergleich der Reaktionen von Elektron-Positron-Paaren zu <a href="/wiki/Hadron" title="Hadron">Hadronen</a> und zu <a href="/wiki/Myon" title="Myon">Myon</a>-Antimyon-Paaren erwartet man naiv in erster Ordnung, dass sich die Streuquerschnitte <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 {BR}}}"> <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">B</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {BR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/707f1a777a37d50b44b9c4d05d33353c7b8ec885" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.514ex; height:2.176ex;" alt="{\displaystyle {\mathcal {BR}}}"></span> zueinander verhalten wie die elektrischen Ladungen <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> der beteiligten Teilchen zum Quadrat, summiert über die verschiedenen Teilchenarten bzw. <a href="/wiki/Flavour" title="Flavour">Flavours</a>: </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 \left.{\frac {{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to {\text{had}})}{{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to \mu ^{+}\mu ^{-})}}\right|_{\text{naiv}}=\left({\frac {\sum _{\text{flavours}}Q_{i}^{2}}{e^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>had</mtext> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">→</mo> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>naiv</mtext> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>flavours</mtext> </mrow> </munder> <msubsup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left.{\frac {{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to {\text{had}})}{{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to \mu ^{+}\mu ^{-})}}\right|_{\text{naiv}}=\left({\frac {\sum _{\text{flavours}}Q_{i}^{2}}{e^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f661d6380a0e99c7d0e5cca39269f971ecf940f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:43.886ex; height:7.509ex;" alt="{\displaystyle \left.{\frac {{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to {\text{had}})}{{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to \mu ^{+}\mu ^{-})}}\right|_{\text{naiv}}=\left({\frac {\sum _{\text{flavours}}Q_{i}^{2}}{e^{2}}}\right)}"></span></dd></dl> <p>mit der <a href="/wiki/Elementarladung" title="Elementarladung">Elementarladung</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 e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span>. </p><p>Experimentell fand man jedoch einen um einen Faktor 3 erhöhten Wert:<sup id="cite_ref-Povh_4-0" class="reference"><a href="#cite_note-Povh-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </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 \left.{\frac {{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to {\text{had}})}{{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to \mu ^{+}\mu ^{-})}}\right|_{\text{exp}}=3\left({\frac {\sum _{\text{flavours}}Q_{i}^{2}}{e^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>had</mtext> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">→</mo> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>exp</mtext> </mrow> </msub> <mo>=</mo> <mn>3</mn> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>flavours</mtext> </mrow> </munder> <msubsup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left.{\frac {{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to {\text{had}})}{{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to \mu ^{+}\mu ^{-})}}\right|_{\text{exp}}=3\left({\frac {\sum _{\text{flavours}}Q_{i}^{2}}{e^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7921f886f94fb09ee8cfd5225e132e4b0ad624c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:44.886ex; height:7.509ex;" alt="{\displaystyle \left.{\frac {{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to {\text{had}})}{{\mathcal {BR}}(\mathrm {e} ^{+}\mathrm {e} ^{-}\to \mu ^{+}\mu ^{-})}}\right|_{\text{exp}}=3\left({\frac {\sum _{\text{flavours}}Q_{i}^{2}}{e^{2}}}\right)}"></span></dd></dl> <p>Das deutet darauf hin, dass Quarks einen zusätzlichen Freiheitsgrad mit drei Ausprägungen innehaben, dass es mit anderen Worten also drei verschiedene Quarks jeden Flavours gibt. Auf der anderen Seite konnte durch <a href="/wiki/Spektroskopisch" class="mw-redirect" title="Spektroskopisch">spektroskopische</a> Messungen ausgeschlossen werden, dass sich die Massen der verschiedenen Quarks desselben Flavours unterscheiden. </p> <div class="mw-heading mw-heading2"><h2 id="Mathematische_Beschreibung">Mathematische Beschreibung</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Farbladung&veaction=edit&section=2" title="Abschnitt bearbeiten: Mathematische Beschreibung" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Farbladung&action=edit&section=2" title="Quellcode des Abschnitts bearbeiten: Mathematische Beschreibung"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Die <a href="/wiki/Symmetriegruppe" title="Symmetriegruppe">Symmetriegruppe</a> der Quantenchromodynamik ist <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 SU(3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SU(3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ac7389c1b06f783c603fa08d057b7c526228519" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.254ex; height:2.843ex;" alt="{\displaystyle SU(3)}"></span>. Die <a href="/w/index.php?title=Fundamentale_Darstellung&action=edit&redlink=1" class="new" title="Fundamentale Darstellung (Seite nicht vorhanden)">fundamentale Darstellung</a> besteht aus komplexen <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 3\times 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\times 3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddc0d4d6106875f8006be1d898512ca5843bad8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.165ex; height:2.176ex;" alt="{\displaystyle 3\times 3}"></span>-Matrizen. Als <a href="/wiki/Lie-Gruppe" title="Lie-Gruppe">Lie-Gruppe</a> der <a href="/wiki/Dimension_(Mathematik)" title="Dimension (Mathematik)">Dimension</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 8}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>8</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 8}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1aaa997e6ad67716cfaa9a02c4df860bf60a95b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 8}"></span> können die <a href="/wiki/Darstellungsmatrix" class="mw-redirect" title="Darstellungsmatrix">Darstellungsmatrizen</a> als <a href="/wiki/Matrixexponential" title="Matrixexponential">Matrixexponential</a> von Elementen einer <a href="/wiki/Lie-Algebra" title="Lie-Algebra">Lie-Algebra</a> mit acht Generatoren geschrieben werden. Diese acht Generatoren sind die <a href="/wiki/Gell-Mann-Matrizen" title="Gell-Mann-Matrizen">Gell-Mann-Matrizen</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 \lambda ^{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ^{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89e7dfb6af28964a99ec1ff1d96eef8057de4f3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.457ex; height:2.343ex;" alt="{\displaystyle \lambda ^{a}}"></span>. </p><p>Eine <a href="/wiki/Eichtransformation" title="Eichtransformation">Eichtransformation</a> wirkt auf ein Fermion <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"> <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/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> vermittels </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 \psi \to \psi '=\exp \left(-\mathrm {i} \sum _{a=1}^{8}\theta ^{a}\lambda ^{a}\right)\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">→</mo> <msup> <mi>ψ</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </munderover> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi \to \psi '=\exp \left(-\mathrm {i} \sum _{a=1}^{8}\theta ^{a}\lambda ^{a}\right)\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a7d75130145ee371a5430a814b3e3477cf61c5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:30.404ex; height:7.509ex;" alt="{\displaystyle \psi \to \psi '=\exp \left(-\mathrm {i} \sum _{a=1}^{8}\theta ^{a}\lambda ^{a}\right)\psi }"></span></dd></dl> <p>mit acht reellen Parametern <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 \theta ^{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta ^{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfd1e92b4c3cb8a1dfc42ba442da8ff86762f11d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.192ex; height:2.343ex;" alt="{\displaystyle \theta ^{a}}"></span>. Aus Dimensionsgründen folgt, dass <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"> <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/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> entweder ein <a href="/wiki/Multiplizit%C3%A4t" title="Multiplizität">Triplett</a> unter dieser Transformation bildet, das heißt, <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"> <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/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> ist ein dreikomponentiger Vektor, oder ein <a href="/wiki/Singulett" class="mw-redirect" title="Singulett">Singulett</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 \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> ist ein Skalar. Das Farbsingulett besteht somit aus Teilchen, auf die die Quantenchromodynamik keine Auswirkungen hat, sie befinden sich in einer trivialen Darstellung. </p><p>Die acht starken Ladungen der Fermionen sind definiert via </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 \rho ^{a}=\psi _{i}^{\dagger }{\tfrac {1}{2}}\lambda _{ij}^{a}\psi _{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mo>=</mo> <msubsup> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <msubsup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ^{a}=\psi _{i}^{\dagger }{\tfrac {1}{2}}\lambda _{ij}^{a}\psi _{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c1e98ddbe17ae4e6112afa47e4b7d6ab40d4dbb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:14.791ex; height:3.843ex;" alt="{\displaystyle \rho ^{a}=\psi _{i}^{\dagger }{\tfrac {1}{2}}\lambda _{ij}^{a}\psi _{j}}"></span></dd></dl> <p>mit den Ladungsdichten <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 \rho ^{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ^{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/381b2dc26e660f689487d4844b27dd86d2f99da8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.304ex; height:2.843ex;" alt="{\displaystyle \rho ^{a}}"></span>. Da die Gell-Mann-Matrizen einer <a href="/wiki/Kommutator_(Mathematik)" title="Kommutator (Mathematik)">Kommutatorrelation</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 [\lambda ^{a},\lambda ^{b}]=2\mathrm {i} f^{abc}\lambda ^{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mo>,</mo> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> <mo stretchy="false">]</mo> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> </mrow> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msup> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [\lambda ^{a},\lambda ^{b}]=2\mathrm {i} f^{abc}\lambda ^{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db408eb6535291afd7945f2742a5e0501cf78372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.124ex; height:3.176ex;" alt="{\displaystyle [\lambda ^{a},\lambda ^{b}]=2\mathrm {i} f^{abc}\lambda ^{c}}"></span> mit den <a href="/wiki/Strukturkonstante" title="Strukturkonstante">Strukturkonstanten</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 f^{abc}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{abc}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9a85bb95b3c37f4338f39fdf6f8c8d9be34d0e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.84ex; height:3.009ex;" alt="{\displaystyle f^{abc}}"></span> der Lie-Algebra folgen, sind die Ladungen nicht <a href="/wiki/Kommensurabilit%C3%A4t_(Quantenmechanik)" title="Kommensurabilität (Quantenmechanik)">gemeinsam messbar</a>. Man muss also eine maximale <a href="/wiki/Untermenge" class="mw-redirect" title="Untermenge">Untermenge</a> kommutierender <a href="/wiki/Observable" title="Observable">Observablen</a> suchen. Dies sind im Fall der starken Ladungen nach Konvention die Komponenten <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^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ec0c38ea3367ecc40cd926d8a31bc7344cd7dc7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.134ex; height:3.009ex;" alt="{\displaystyle q^{3}}"></span> und <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^{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q^{8}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2089376c7cb70c013dcbe3c11dd071b6e8054fc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.134ex; height:3.009ex;" alt="{\displaystyle q^{8}}"></span>; die Matrizen <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 \lambda ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b0db8dc15468a0e5f50aafeec621053c243b0b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.409ex; height:2.676ex;" alt="{\displaystyle \lambda ^{3}}"></span> und <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 \lambda ^{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ^{8}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51512839a345813b33568ea3f76986d425656830" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.409ex; height:2.676ex;" alt="{\displaystyle \lambda ^{8}}"></span> sind <a href="/wiki/Diagonalmatrix" title="Diagonalmatrix">diagonal</a>. Der gemeinsame Satz <a href="/wiki/Eigenvektor" class="mw-redirect" title="Eigenvektor">Eigenvektoren</a> zu <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 \lambda ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b0db8dc15468a0e5f50aafeec621053c243b0b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.409ex; height:2.676ex;" alt="{\displaystyle \lambda ^{3}}"></span> und <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 \lambda ^{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ^{8}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51512839a345813b33568ea3f76986d425656830" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.409ex; height:2.676ex;" alt="{\displaystyle \lambda ^{8}}"></span> sind die drei Farben </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 {\begin{aligned}\psi _{r}={\vec {r}}\otimes \psi ={\begin{pmatrix}1\\0\\0\end{pmatrix}}\otimes \psi \\\psi _{g}={\vec {g}}\otimes \psi ={\begin{pmatrix}0\\1\\0\end{pmatrix}}\otimes \psi \\\psi _{b}={\vec {b}}\otimes \psi ={\begin{pmatrix}0\\0\\1\end{pmatrix}}\otimes \psi \end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⊗</mo> <mi>ψ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>⊗</mo> <mi>ψ</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⊗</mo> <mi>ψ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>⊗</mo> <mi>ψ</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⊗</mo> <mi>ψ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>⊗</mo> <mi>ψ</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\psi _{r}={\vec {r}}\otimes \psi ={\begin{pmatrix}1\\0\\0\end{pmatrix}}\otimes \psi \\\psi _{g}={\vec {g}}\otimes \psi ={\begin{pmatrix}0\\1\\0\end{pmatrix}}\otimes \psi \\\psi _{b}={\vec {b}}\otimes \psi ={\begin{pmatrix}0\\0\\1\end{pmatrix}}\otimes \psi \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4bd1e57b87ac82a775cb007d52b65f9e562a67d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -13.671ex; width:25.346ex; height:28.509ex;" alt="{\displaystyle {\begin{aligned}\psi _{r}={\vec {r}}\otimes \psi ={\begin{pmatrix}1\\0\\0\end{pmatrix}}\otimes \psi \\\psi _{g}={\vec {g}}\otimes \psi ={\begin{pmatrix}0\\1\\0\end{pmatrix}}\otimes \psi \\\psi _{b}={\vec {b}}\otimes \psi ={\begin{pmatrix}0\\0\\1\end{pmatrix}}\otimes \psi \end{aligned}}}"></span></dd></dl> <p>mit den Bezeichnungen <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 r,g,b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>,</mo> <mi>g</mi> <mo>,</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r,g,b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ee113645ded7792b74bf69857df5229a2847934" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.23ex; height:2.509ex;" alt="{\displaystyle r,g,b}"></span> für rot, grün und blau. </p><p>Die starke Ladung eines roten, grünen und blauen Teilchens ist entsprechend </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 {\begin{alignedat}{2}{\vec {q}}_{r}&=+{\frac {1}{2}}{\vec {e}}_{3}&&+{\frac {1}{2{\sqrt {3}}}}{\vec {e}}_{8}\\{\vec {q}}_{g}&=-{\frac {1}{2}}{\vec {e}}_{3}&&+{\frac {1}{2{\sqrt {3}}}}{\vec {e}}_{8}\\{\vec {q}}_{b}&=&&-{\frac {1}{\sqrt {3}}}{\vec {e}}_{8}\end{alignedat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left" rowspacing="3pt" columnspacing="0em 0em 0em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>e</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <mi></mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>e</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>e</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <mi></mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>e</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> </mtd> <mtd /> <mtd> <mi></mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>3</mn> </msqrt> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>e</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{alignedat}{2}{\vec {q}}_{r}&=+{\frac {1}{2}}{\vec {e}}_{3}&&+{\frac {1}{2{\sqrt {3}}}}{\vec {e}}_{8}\\{\vec {q}}_{g}&=-{\frac {1}{2}}{\vec {e}}_{3}&&+{\frac {1}{2{\sqrt {3}}}}{\vec {e}}_{8}\\{\vec {q}}_{b}&=&&-{\frac {1}{\sqrt {3}}}{\vec {e}}_{8}\end{alignedat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84d1636032b77d41584cbfcbf168081dc54de516" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.564ex; margin-bottom: -0.274ex; width:22.479ex; height:18.843ex;" alt="{\displaystyle {\begin{alignedat}{2}{\vec {q}}_{r}&=+{\frac {1}{2}}{\vec {e}}_{3}&&+{\frac {1}{2{\sqrt {3}}}}{\vec {e}}_{8}\\{\vec {q}}_{g}&=-{\frac {1}{2}}{\vec {e}}_{3}&&+{\frac {1}{2{\sqrt {3}}}}{\vec {e}}_{8}\\{\vec {q}}_{b}&=&&-{\frac {1}{\sqrt {3}}}{\vec {e}}_{8}\end{alignedat}}}"></span></dd></dl> <p>und eine Addition eines roten, grünen und blauen Teilchens ergibt insgesamt ein unter der starken Ladung neutrales Objekt. </p><p>Die <a href="/wiki/Antiteilchen" title="Antiteilchen">Antiteilchen</a> transformieren unter der <a href="/w/index.php?title=Konjugierte_Darstellung&action=edit&redlink=1" class="new" title="Konjugierte Darstellung (Seite nicht vorhanden)">konjugierten Darstellung</a>; die Farbvektoren sind </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 {\begin{aligned}{\vec {c}}={\begin{pmatrix}1&0&0\end{pmatrix}}\\{\vec {m}}={\begin{pmatrix}0&1&0\end{pmatrix}}\\{\vec {y}}={\begin{pmatrix}0&0&1\end{pmatrix}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>c</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\vec {c}}={\begin{pmatrix}1&0&0\end{pmatrix}}\\{\vec {m}}={\begin{pmatrix}0&1&0\end{pmatrix}}\\{\vec {y}}={\begin{pmatrix}0&0&1\end{pmatrix}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c51bf9ff7237c0e4e76e94e27632483f9fe3fd5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:16.584ex; height:9.176ex;" alt="{\displaystyle {\begin{aligned}{\vec {c}}={\begin{pmatrix}1&0&0\end{pmatrix}}\\{\vec {m}}={\begin{pmatrix}0&1&0\end{pmatrix}}\\{\vec {y}}={\begin{pmatrix}0&0&1\end{pmatrix}}\end{aligned}}}"></span></dd></dl> <p>entsprechend den Sekundärfarben <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,m,y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c,m,y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/436338aa2783b1bf19c61af20db1eadeccf89bb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.271ex; height:2.009ex;" alt="{\displaystyle c,m,y}"></span> für <a href="/wiki/Cyan" title="Cyan">cyan</a>, <a href="/wiki/Magenta_(Farbe)" title="Magenta (Farbe)">magenta</a> und gelb (yellow). </p> <div class="mw-heading mw-heading3"><h3 id="Beschreibung_der_Gluonen">Beschreibung der Gluonen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Farbladung&veaction=edit&section=3" title="Abschnitt bearbeiten: Beschreibung der Gluonen" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Farbladung&action=edit&section=3" title="Quellcode des Abschnitts bearbeiten: Beschreibung der Gluonen"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Die Gluonen transformieren unter Eichtransformationen in der <a href="/wiki/Adjungierte_Darstellung" title="Adjungierte Darstellung">adjungierten Darstellung</a> der Symmetriegruppe. Die Darstellungsmatrizen sind die Strukturkonstanten, also <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 {f^{a}}_{bc}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {f^{a}}_{bc}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/842e579acc6fccab584633dc0322757db1c6fb79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.072ex; height:2.843ex;" alt="{\displaystyle {f^{a}}_{bc}}"></span>, und die Eichtransformation lautet </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 A^{\mu a}\to A'^{\mu a}=A^{\mu a}-{\frac {1}{g}}\partial ^{\mu }\theta ^{a}+f^{abc}\theta ^{b}A^{\mu c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>a</mi> </mrow> </msup> <mo stretchy="false">→</mo> <msup> <mi>A</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>a</mi> </mrow> </mrow> </msup> <mo>=</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>a</mi> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>g</mi> </mfrac> </mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msup> <msup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>c</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{\mu a}\to A'^{\mu a}=A^{\mu a}-{\frac {1}{g}}\partial ^{\mu }\theta ^{a}+f^{abc}\theta ^{b}A^{\mu c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e4051a6d293352cd99f52a7e2bca9a463bcf93b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:40.658ex; height:5.676ex;" alt="{\displaystyle A^{\mu a}\to A'^{\mu a}=A^{\mu a}-{\frac {1}{g}}\partial ^{\mu }\theta ^{a}+f^{abc}\theta ^{b}A^{\mu c}}"></span>,</dd></dl> <p>woraus offensichtlich wird, dass acht an der starken Wechselwirkung teilnehmende Gluonen existieren; sie bilden ein Oktett. </p><p>Dargestellt werden die Gluonen im Farbraum als <a href="/wiki/Linear_unabh%C3%A4ngig" class="mw-redirect" title="Linear unabhängig">linear unabhängige</a> <a href="/wiki/Spur_(Mathematik)" title="Spur (Mathematik)">spur</a>freie <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 3\times 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\times 3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddc0d4d6106875f8006be1d898512ca5843bad8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.165ex; height:2.176ex;" alt="{\displaystyle 3\times 3}"></span>-Matrizen, formal als <a href="/wiki/Tensorprodukt" title="Tensorprodukt">Tensorprodukt</a> aus einer Farbe und einer Antifarbe. Sie können so gewählt werden, dass sie (bis auf Normierung) den Gell-Mann-Matrizen entsprechen. Beispielsweise ist </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 A_{ij}^{\mu 1}=(r_{i}m_{j}+g_{i}c_{j})/{\sqrt {2}}\otimes A^{\mu }=\lambda _{ij}^{1}/{\sqrt {2}}\otimes A^{\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>⊗</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mo>=</mo> <msubsup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>⊗</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{ij}^{\mu 1}=(r_{i}m_{j}+g_{i}c_{j})/{\sqrt {2}}\otimes A^{\mu }=\lambda _{ij}^{1}/{\sqrt {2}}\otimes A^{\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92df2142a15b2b9d3ca42c8615bb59969d25e099" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:46.227ex; height:3.843ex;" alt="{\displaystyle A_{ij}^{\mu 1}=(r_{i}m_{j}+g_{i}c_{j})/{\sqrt {2}}\otimes A^{\mu }=\lambda _{ij}^{1}/{\sqrt {2}}\otimes A^{\mu }}"></span></dd></dl> <p>eine <a href="/wiki/Superposition_(Physik)" title="Superposition (Physik)">Superposition</a> aus rot-magenta und grün-cyan. </p><p>Das „neunte“ Gluon wäre </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 A_{ij}^{\mu 9}=(r_{i}c_{j}+g_{i}m_{j}+b_{i}y_{j})/{\sqrt {3}}\otimes A^{\mu }=I_{3}/{\sqrt {3}}\otimes A^{\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mn>9</mn> </mrow> </msubsup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>⊗</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>⊗</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{ij}^{\mu 9}=(r_{i}c_{j}+g_{i}m_{j}+b_{i}y_{j})/{\sqrt {3}}\otimes A^{\mu }=I_{3}/{\sqrt {3}}\otimes A^{\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c446f303d79c1a7803a6c563aca468a19991b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:52.158ex; height:3.843ex;" alt="{\displaystyle A_{ij}^{\mu 9}=(r_{i}c_{j}+g_{i}m_{j}+b_{i}y_{j})/{\sqrt {3}}\otimes A^{\mu }=I_{3}/{\sqrt {3}}\otimes A^{\mu }}"></span></dd></dl> <p>mit der dreidimensionalen <a href="/wiki/Einheitsmatrix" title="Einheitsmatrix">Einheitsmatrix</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 I_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/becba5d3350c4dd244f3cda48eb13439f21ed350" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{3}}"></span> und somit ein Singulett unter der <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 SU(3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SU(3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ac7389c1b06f783c603fa08d057b7c526228519" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.254ex; height:2.843ex;" alt="{\displaystyle SU(3)}"></span>. Es nähme nicht an der starken Wechselwirkung teil und wäre somit ein <a href="/w/index.php?title=Steriles_Teilchen&action=edit&redlink=1" class="new" title="Steriles Teilchen (Seite nicht vorhanden)">steriles Teilchen</a>. Versuche, das neunte Gluon als das <a href="/wiki/Photon" title="Photon">Photon</a> zu interpretieren, also als das <a href="/wiki/Eichboson" title="Eichboson">Eichboson</a> der <a href="/wiki/Elektromagnetische_Wechselwirkung" title="Elektromagnetische Wechselwirkung">elektromagnetischen Wechselwirkung</a>, scheiterten. </p> <div class="mw-heading mw-heading2"><h2 id="Singuletts_und_Confinement">Singuletts und Confinement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Farbladung&veaction=edit&section=4" title="Abschnitt bearbeiten: Singuletts und Confinement" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Farbladung&action=edit&section=4" title="Quellcode des Abschnitts bearbeiten: Singuletts und Confinement"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hauptartikel" role="navigation"><span class="hauptartikel-pfeil" title="siehe" aria-hidden="true" role="presentation">→ </span><i><span class="hauptartikel-text">Hauptartikel</span>: <a href="/wiki/Confinement" title="Confinement">Confinement</a></i></div> <p>Experimentell können keine <a href="/wiki/Freies_Teilchen" title="Freies Teilchen">freien</a> Gluonen oder Quarks beobachtet werden; sie sind confined (engl.: <i>eingesperrt</i>). Die Kraft, die für das Confinement verantwortlich ist, ist die <a href="/wiki/Starke_Kernkraft" class="mw-redirect" title="Starke Kernkraft">starke Kernkraft</a>, die mit zunehmendem Abstand <i>wächst</i>: Versucht man, ein Quark aus einem Hadron zu befreien, wird ein Quark-Antiquark-Paar gebildet, sodass zwei neue Hadronen entstehen. Die beobachtbaren physikalischen Objekte, die aus Gluonen oder Quarks aufgebaut sind, müssen daher <a href="/wiki/Singulett" class="mw-redirect" title="Singulett">Singuletts</a> unter der <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 SU(3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SU(3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ac7389c1b06f783c603fa08d057b7c526228519" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.254ex; height:2.843ex;" alt="{\displaystyle SU(3)}"></span> sein. </p><p>Die drei erlaubten Kombinationen, die zu Singuletts führen, sind: </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 {\begin{aligned}\Psi _{\mathrm {B} }&={\frac {1}{\sqrt {6}}}\varepsilon _{abc}\psi _{a}\psi _{b}\psi _{c}\\\Psi _{\bar {\mathrm {B} }}&={\frac {1}{\sqrt {6}}}\varepsilon _{abc}{\bar {\psi }}_{a}{\bar {\psi }}_{b}{\bar {\psi }}_{c}\\\Psi _{\mathrm {M} }&={\frac {1}{\sqrt {3}}}{\bar {\psi }}_{a}\psi _{a}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>6</mn> </msqrt> </mfrac> </mrow> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msub> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>6</mn> </msqrt> </mfrac> </mrow> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>3</mn> </msqrt> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\Psi _{\mathrm {B} }&={\frac {1}{\sqrt {6}}}\varepsilon _{abc}\psi _{a}\psi _{b}\psi _{c}\\\Psi _{\bar {\mathrm {B} }}&={\frac {1}{\sqrt {6}}}\varepsilon _{abc}{\bar {\psi }}_{a}{\bar {\psi }}_{b}{\bar {\psi }}_{c}\\\Psi _{\mathrm {M} }&={\frac {1}{\sqrt {3}}}{\bar {\psi }}_{a}\psi _{a}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/848af991c4dbb8756dd8d6ecdef3721047da720a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.564ex; margin-bottom: -0.274ex; width:22.705ex; height:18.843ex;" alt="{\displaystyle {\begin{aligned}\Psi _{\mathrm {B} }&={\frac {1}{\sqrt {6}}}\varepsilon _{abc}\psi _{a}\psi _{b}\psi _{c}\\\Psi _{\bar {\mathrm {B} }}&={\frac {1}{\sqrt {6}}}\varepsilon _{abc}{\bar {\psi }}_{a}{\bar {\psi }}_{b}{\bar {\psi }}_{c}\\\Psi _{\mathrm {M} }&={\frac {1}{\sqrt {3}}}{\bar {\psi }}_{a}\psi _{a}\end{aligned}}}"></span></dd></dl> <p>mit </p> <ul><li>dem <a href="/wiki/Levi-Civita-Symbol" title="Levi-Civita-Symbol">Levi-Civita-Symbol</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 \varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }"></span></li> <li>einer <a href="/wiki/Baryon" title="Baryon">baryonischen</a>, aus drei Quarks aufgebauten Wellenfunktion <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 _{\mathrm {B} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{\mathrm {B} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3c9f2051090b45b8d05232421d940ba8f5e59e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.204ex; height:2.509ex;" alt="{\displaystyle \Psi _{\mathrm {B} }}"></span></li> <li>einer <a href="/wiki/Antiteilchen" title="Antiteilchen">antibaryonischen</a>, aus drei <a href="/wiki/Antiquark" class="mw-redirect" title="Antiquark">Antiquarks</a> aufgebauten Wellenfunktion <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 _{\bar {\mathrm {B} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{\bar {\mathrm {B} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5d40f9895955b73e9a0a84c4c059469d39e9359" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.204ex; height:2.676ex;" alt="{\displaystyle \Psi _{\bar {\mathrm {B} }}}"></span></li> <li><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 _{\mathrm {M} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{\mathrm {M} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4428dcce168069e2c95044760630aa493b8616be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.547ex; height:2.509ex;" alt="{\displaystyle \Psi _{\mathrm {M} }}"></span> eine <a href="/wiki/Meson" title="Meson">mesonische</a> Wellenfunktion, aufgebaut aus Quark-Antiquark-Paaren.</li></ul> <p>Darüber hinaus können theoretisch exotische Strukturen auftreten wie <a href="/wiki/Tetraquark" title="Tetraquark">Tetraquarks</a>, <a href="/wiki/Pentaquark" title="Pentaquark">Pentaquarks</a> oder Teilchen mit höherem Quarkinhalt, die sich aus den obigen Zuständen zusammensetzen lassen, sowie <a href="/wiki/Glueball" title="Glueball">Glueballs</a> als rein gluonische Strukturen. Auf die Existenz von Tetraquarks existieren experimentelle Hinweise am <a href="/wiki/Forschungszentrum_J%C3%BClich#Kühlersynchrotron_COSY" title="Forschungszentrum Jülich">COSY</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>, jedoch nicht auf die Existenz von Glueballs. </p><p>Die Struktur der <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 SU(3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SU(3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ac7389c1b06f783c603fa08d057b7c526228519" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.254ex; height:2.843ex;" alt="{\displaystyle SU(3)}"></span> als nichtabelsche <a href="/wiki/Eichtheorie" title="Eichtheorie">Eichtheorie</a> ist auch dafür verantwortlich, dass die starke Wechselwirkung so kurzreichweitig ist, obwohl die Gluonen masselos sind wie die Photonen der <a href="/wiki/Quantenelektrodynamik" title="Quantenelektrodynamik">Quantenelektrodynamik</a>: Da die Gluonen als adjungierte Repräsentation der <a href="/wiki/Eichgruppe" title="Eichgruppe">Eichgruppe</a> selbst Farbe tragen, wechselwirken sie mit sich selbst. In der <a href="/wiki/U(1)" class="mw-redirect" title="U(1)"><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 U(1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e62b00d74ee0cefb86cc052365625abff56d43e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.754ex; height:2.843ex;" alt="{\displaystyle U(1)}"></span></a> der Elektrodynamik dagegen fallen triviale und adjungierte Darstellung zusammen, sodass Photonen sich <i>nicht</i> gegenseitig beeinflussen. </p> <div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Farbladung&veaction=edit&section=5" title="Abschnitt bearbeiten: Weblinks" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Farbladung&action=edit&section=5" title="Quellcode des Abschnitts bearbeiten: Weblinks"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.scholarpedia.org/article/Color_charge">O. W. Greenberg: Color charge</a>, Scholarpedia</li></ul> <div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Farbladung&veaction=edit&section=6" title="Abschnitt bearbeiten: Literatur" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Farbladung&action=edit&section=6" title="Quellcode des Abschnitts bearbeiten: Literatur"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Ian J. R. Aitchison und Anthony J. G. Hey: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Gauge Theories in Particle Physics</cite>. 2. Auflage. Institute of Physics Publishing, Bristol 1989, <a href="/wiki/Spezial:ISBN-Suche/0852743297" class="internal mw-magiclink-isbn">ISBN 0-85274-329-7</a>, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>281–288</span> (englisch).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Farbladung&rft.au=Ian+J.+R.+Aitchison+und+Anthony+J.+G.+Hey&rft.btitle=Gauge+Theories+in+Particle+Physics&rft.date=1989&rft.edition=2&rft.genre=book&rft.isbn=0852743297&rft.pages=281-288&rft.place=Bristol&rft.pub=Institute+of+Physics+Publishing" style="display:none"> </span></li> <li>Peter Becher, Manfred Böhm und Hans Joos: <cite style="font-style:italic">Eichtheorien der starken und elektroschwachen Wechselwirkung</cite>. 2. Auflage. Vieweg+Teubner, 1983, <a href="/wiki/Spezial:ISBN-Suche/9783519130451" class="internal mw-magiclink-isbn">ISBN 978-3-519-13045-1</a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Farbladung&rft.au=Peter+Becher%2C+Manfred+B%C3%B6hm+und+Hans+Joos&rft.btitle=Eichtheorien+der+starken+und+elektroschwachen+Wechselwirkung&rft.date=1983&rft.edition=2&rft.genre=book&rft.isbn=9783519130451&rft.pub=Vieweg%2BTeubner" style="display:none"> </span></li> <li>David Griffiths: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Introduction to Elementary Particle Physics</cite>. John Wiley & Sons, New York 1987, <a href="/wiki/Spezial:ISBN-Suche/0471603864" class="internal mw-magiclink-isbn">ISBN 0-471-60386-4</a> (englisch).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Farbladung&rft.au=David+Griffiths&rft.btitle=Introduction+to+Elementary+Particle+Physics&rft.date=1987&rft.genre=book&rft.isbn=0471603864&rft.place=New+York&rft.pub=John+Wiley+%26+Sons" style="display:none"> </span></li> <li>Jarrett L. Lancaster: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Introduction to Classical Field Theory: A Tour of the fundamental interactions</cite>. Morgan & Claypool, San Rafael, <a href="/wiki/Spezial:ISBN-Suche/9781643270814" class="internal mw-magiclink-isbn">ISBN 978-1-64327-081-4</a>, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>4.8–4.12</span> (englisch).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Farbladung&rft.au=Jarrett+L.+Lancaster&rft.btitle=Introduction+to+Classical+Field+Theory%3A+A+Tour+of+the+fundamental+interactions&rft.genre=book&rft.isbn=9781643270814&rft.pages=4.8-4.12&rft.place=San+Rafael&rft.pub=Morgan+%26+Claypool" style="display:none"> </span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Farbladung&veaction=edit&section=7" title="Abschnitt bearbeiten: Einzelnachweise" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Farbladung&action=edit&section=7" title="Quellcode des Abschnitts bearbeiten: Einzelnachweise"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Oscar W. Greenberg: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Spin and Unitary-Spin Independence in a Paraquark Model of Baryons and Mesons</cite>. In: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Physical Review Letters</cite>. <span style="white-space:nowrap">Band<span style="display:inline-block;width:.2em"> </span>13</span>, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>20</span>, 1964, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>598–602</span> (englisch).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Farbladung&rft.atitle=Spin+and+Unitary-Spin+Independence+in+a+Paraquark+Model+of+Baryons+and+Mesons&rft.au=Oscar+W.+Greenberg&rft.date=1964&rft.genre=journal&rft.issue=20&rft.jtitle=Physical+Review+Letters&rft.pages=598-602&rft.volume=13" style="display:none"> </span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Moo-Young Han und Yoichiro Nambu: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Three-Triplet Model with Double SU(3) Symmetry</cite>. In: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Physical Review</cite>. <span style="white-space:nowrap">Band<span style="display:inline-block;width:.2em"> </span>139</span>, 4B, 1965, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>B 1006–B 1010</span> (englisch).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Farbladung&rft.atitle=Three-Triplet+Model+with+Double+SU%283%29+Symmetry&rft.au=Moo-Young+Han+und+Yoichiro+Nambu&rft.date=1965&rft.genre=journal&rft.issue=4B&rft.jtitle=Physical+Review&rft.pages=B+1006-B+1010&rft.volume=139" style="display:none"> </span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Richard P. Feynman: <cite style="font-style:italic">QED: The Strange Theory of Light and Matter</cite>. Princeton University Press, Princeton Oxford 2006, <a href="/wiki/Spezial:ISBN-Suche/9780691125756" class="internal mw-magiclink-isbn">ISBN 978-0-691-12575-6</a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Farbladung&rft.au=Richard+P.+Feynman&rft.btitle=QED%3A+The+Strange+Theory+of+Light+and+Matter&rft.date=2006&rft.genre=book&rft.isbn=9780691125756&rft.place=Princeton+Oxford&rft.pub=Princeton+University+Press" style="display:none"> </span></span> </li> <li id="cite_note-Povh-4"><span class="mw-cite-backlink"><a href="#cite_ref-Povh_4-0">↑</a></span> <span class="reference-text"><a href="/wiki/Bogdan_Povh" title="Bogdan Povh">Bogdan Povh</a>, <a href="/wiki/Klaus_Rith" title="Klaus Rith">Klaus Rith</a>, Christoph Scholz, Frank Zetsche: <i>Teilchen und Kerne.</i> 8. Auflage. Springer, Berlin 2009, <a href="/wiki/Spezial:ISBN-Suche/9783540680758" class="internal mw-magiclink-isbn">ISBN 978-3-540-68075-8</a>.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">WASA-at-COSY Collaboration: <cite style="font-style:italic">Evidence for a New Resonance from Polarized Neutron-Proton Scattering</cite>. In: <cite style="font-style:italic">Physical Review Letters</cite>. <span style="white-space:nowrap">Band<span style="display:inline-block;width:.2em"> </span>112</span>, 2014, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>202401<span style="display:inline-block;width:.2em"> </span>ff</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Farbladung&rft.atitle=Evidence+for+a+New+Resonance+from+Polarized+Neutron-Proton+Scattering&rft.au=WASA-at-COSY+Collaboration&rft.btitle=Physical+Review+Letters&rft.date=2014&rft.genre=book&rft.pages=202401ff.&rft.volume=112" style="display:none"> </span></span> </li> </ol></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Abgerufen von „<a dir="ltr" href="https://de.wikipedia.org/w/index.php?title=Farbladung&oldid=236726708">https://de.wikipedia.org/w/index.php?title=Farbladung&oldid=236726708</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Wikipedia:Kategorien" title="Wikipedia:Kategorien">Kategorien</a>: <ul><li><a href="/wiki/Kategorie:Teilchenphysik" title="Kategorie:Teilchenphysik">Teilchenphysik</a></li><li><a href="/wiki/Kategorie:Quantenfeldtheorie" title="Kategorie:Quantenfeldtheorie">Quantenfeldtheorie</a></li></ul></div></div> </div> </div> <div id="mw-navigation"> <h2>Navigationsmenü</h2> <div id="mw-head"> <nav id="p-personal" class="mw-portlet mw-portlet-personal vector-user-menu-legacy vector-menu" aria-labelledby="p-personal-label" > <h3 id="p-personal-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Meine Werkzeuge</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anonuserpage" class="mw-list-item"><span title="Benutzerseite der IP-Adresse, von der aus du Änderungen durchführst">Nicht angemeldet</span></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spezial:Meine_Diskussionsseite" title="Diskussion über Änderungen von dieser IP-Adresse [n]" accesskey="n"><span>Diskussionsseite</span></a></li><li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Spezial:Meine_Beitr%C3%A4ge" title="Eine Liste der Bearbeitungen, die von dieser IP-Adresse gemacht wurden [y]" accesskey="y"><span>Beiträge</span></a></li><li id="pt-createaccount" class="mw-list-item"><a href="/w/index.php?title=Spezial:Benutzerkonto_anlegen&returnto=Farbladung" title="Wir ermutigen dich dazu, ein Benutzerkonto zu erstellen und dich anzumelden. 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href="https://ar.wikipedia.org/wiki/%D8%B4%D8%AD%D9%86%D8%A9_%D9%84%D9%88%D9%86%D9%8A%D8%A9" title="شحنة لونية – Arabisch" lang="ar" hreflang="ar" data-title="شحنة لونية" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BB%D0%B5%D1%80_(%D0%BA%D0%B2%D0%B0%D0%BD%D1%82%D0%B0%D0%B2%D0%B0%D1%8F_%D1%85%D1%80%D0%BE%D0%BC%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0)" title="Колер (квантавая хромадынаміка) – Belarussisch" lang="be" hreflang="be" data-title="Колер (квантавая хромадынаміка)" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" 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%A6%D0%B2%D0%B5%D1%82%D0%B5%D0%BD_%D0%B7%D0%B0%D1%80%D1%8F%D0%B4" title="Цветен заряд – Bulgarisch" lang="bg" hreflang="bg" data-title="Цветен заряд" data-language-autonym="Български" data-language-local-name="Bulgarisch" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kolor_naboj" title="Kolor naboj – Bosnisch" lang="bs" hreflang="bs" data-title="Kolor naboj" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" 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/C%C3%A0rrega_de_color" title="Càrrega de color – Katalanisch" lang="ca" hreflang="ca" data-title="Càrrega de color" data-language-autonym="Català" data-language-local-name="Katalanisch" 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/Barevn%C3%BD_n%C3%A1boj" title="Barevný náboj – Tschechisch" lang="cs" hreflang="cs" data-title="Barevný náboj" data-language-autonym="Čeština" data-language-local-name="Tschechisch" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%C4%95%D1%81_(%D0%BA%D0%B2%D0%B0%D0%BD%D1%82%D0%BB%D0%B0_%D1%85%D0%B8%D1%81%D0%B5%D0%BF)" title="Тĕс (квантла хисеп) – Tschuwaschisch" lang="cv" hreflang="cv" data-title="Тĕс (квантла хисеп)" data-language-autonym="Чӑвашла" data-language-local-name="Tschuwaschisch" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Farveladning" title="Farveladning – Dänisch" lang="da" hreflang="da" data-title="Farveladning" data-language-autonym="Dansk" data-language-local-name="Dänisch" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Color_charge" title="Color charge – Englisch" lang="en" hreflang="en" data-title="Color charge" data-language-autonym="English" data-language-local-name="Englisch" 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/Kolor%C5%9Dargo" title="Kolorŝargo – Esperanto" lang="eo" hreflang="eo" data-title="Kolorŝargo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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/Carga_de_color" title="Carga de color – Spanisch" lang="es" hreflang="es" data-title="Carga de color" data-language-autonym="Español" data-language-local-name="Spanisch" 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/V%C3%A4rvilaeng" title="Värvilaeng – Estnisch" lang="et" hreflang="et" data-title="Värvilaeng" data-language-autonym="Eesti" data-language-local-name="Estnisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kolore_karga" title="Kolore karga – Baskisch" lang="eu" hreflang="eu" data-title="Kolore karga" data-language-autonym="Euskara" data-language-local-name="Baskisch" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D8%A7%D8%B1_%D8%B1%D9%86%DA%AF" title="بار رنگ – Persisch" lang="fa" hreflang="fa" data-title="بار رنگ" data-language-autonym="فارسی" data-language-local-name="Persisch" 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/V%C3%A4rivaraus" title="Värivaraus – Finnisch" lang="fi" hreflang="fi" data-title="Värivaraus" data-language-autonym="Suomi" data-language-local-name="Finnisch" 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/Charge_de_couleur" title="Charge de couleur – Französisch" lang="fr" hreflang="fr" data-title="Charge de couleur" data-language-autonym="Français" data-language-local-name="Französisch" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%98%D7%A2%D7%9F_%D7%A6%D7%91%D7%A2" title="מטען צבע – Hebräisch" lang="he" hreflang="he" data-title="מטען צבע" data-language-autonym="עברית" data-language-local-name="Hebräisch" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Naboj_boje" title="Naboj boje – Kroatisch" lang="hr" hreflang="hr" data-title="Naboj boje" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" 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/Sz%C3%ADnt%C3%B6lt%C3%A9s" title="Színtöltés – Ungarisch" lang="hu" hreflang="hu" data-title="Színtöltés" data-language-autonym="Magyar" data-language-local-name="Ungarisch" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Carica_di_colore" title="Carica di colore – Italienisch" lang="it" hreflang="it" data-title="Carica di colore" data-language-autonym="Italiano" data-language-local-name="Italienisch" 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/%E3%82%AB%E3%83%A9%E3%83%BC%E3%83%81%E3%83%A3%E3%83%BC%E3%82%B8" title="カラーチャージ – Japanisch" lang="ja" hreflang="ja" data-title="カラーチャージ" data-language-autonym="日本語" data-language-local-name="Japanisch" 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%A4%E1%83%94%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%A3%E1%83%AE%E1%83%A2%E1%83%98" title="ფერის მუხტი – Georgisch" lang="ka" hreflang="ka" data-title="ფერის მუხტი" data-language-autonym="ქართული" data-language-local-name="Georgisch" 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%83%89%EC%A0%84%ED%95%98" title="색전하 – Koreanisch" lang="ko" hreflang="ko" data-title="색전하" data-language-autonym="한국어" data-language-local-name="Koreanisch" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B0%E0%A4%82%E0%A4%97%E0%A4%AD%E0%A4%BE%E0%A4%B0" title="रंगभार – Marathi" lang="mr" hreflang="mr" data-title="रंगभार" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Cas_warna" title="Cas warna – Malaiisch" lang="ms" hreflang="ms" data-title="Cas warna" data-language-autonym="Bahasa Melayu" data-language-local-name="Malaiisch" 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/Kleurlading" title="Kleurlading – Niederländisch" lang="nl" hreflang="nl" data-title="Kleurlading" data-language-autonym="Nederlands" data-language-local-name="Niederländisch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%C5%81adunek_kolorowy" title="Ładunek kolorowy – Polnisch" lang="pl" hreflang="pl" data-title="Ładunek kolorowy" data-language-autonym="Polski" data-language-local-name="Polnisch" 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/Carga_de_cor" title="Carga de cor – Portugiesisch" lang="pt" hreflang="pt" data-title="Carga de cor" data-language-autonym="Português" data-language-local-name="Portugiesisch" 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/Sarcin%C4%83_de_culoare" title="Sarcină de culoare – Rumänisch" lang="ro" hreflang="ro" data-title="Sarcină de culoare" data-language-autonym="Română" data-language-local-name="Rumänisch" 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%A6%D0%B2%D0%B5%D1%82%D0%BE%D0%B2%D0%BE%D0%B9_%D0%B7%D0%B0%D1%80%D1%8F%D0%B4" title="Цветовой заряд – Russisch" lang="ru" hreflang="ru" data-title="Цветовой заряд" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Farba_(kvantov%C3%A1_fyzika)" title="Farba (kvantová fyzika) – Slowakisch" lang="sk" hreflang="sk" data-title="Farba (kvantová fyzika)" data-language-autonym="Slovenčina" data-language-local-name="Slowakisch" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Barvni_naboj" title="Barvni naboj – Slowenisch" lang="sl" hreflang="sl" data-title="Barvni naboj" data-language-autonym="Slovenščina" data-language-local-name="Slowenisch" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/F%C3%A4rgladdning" title="Färgladdning – Schwedisch" lang="sv" hreflang="sv" data-title="Färgladdning" data-language-autonym="Svenska" data-language-local-name="Schwedisch" 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/Renk_y%C3%BCk%C3%BC" title="Renk yükü – Türkisch" lang="tr" hreflang="tr" data-title="Renk yükü" data-language-autonym="Türkçe" data-language-local-name="Türkisch" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/T%C3%B6sle_qor%C4%9F%C4%B1" title="Tösle qorğı – Tatarisch" lang="tt" hreflang="tt" data-title="Tösle qorğı" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatarisch" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BB%D1%8C%D0%BE%D1%80%D0%BE%D0%B2%D0%B8%D0%B9_%D0%B7%D0%B0%D1%80%D1%8F%D0%B4" title="Кольоровий заряд – Ukrainisch" lang="uk" hreflang="uk" data-title="Кольоровий заряд" data-language-autonym="Українська" data-language-local-name="Ukrainisch" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Rang_zaryadi" title="Rang zaryadi – Usbekisch" lang="uz" hreflang="uz" data-title="Rang zaryadi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Usbekisch" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%C3%A0u_t%C3%ADch" title="Màu tích – Vietnamesisch" lang="vi" hreflang="vi" data-title="Màu tích" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamesisch" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%89%B2%E8%8D%B7" title="色荷 – Wu" lang="wuu" hreflang="wuu" data-title="色荷" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%89%B2%E8%8D%B7" title="色荷 – Chinesisch" lang="zh" hreflang="zh" data-title="色荷" data-language-autonym="中文" data-language-local-name="Chinesisch" 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Farbladung – Wikipedia