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1955)</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Luis Álvarez-Gaumé</div></th></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="birthplace"><a href="/wiki/Madrid" title="Madrid">Madrid</a>, Spain</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><a href="/wiki/Spaniards" title="Spaniards">Spanish</a></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/Stony_Brook_University" title="Stony Brook University">Stony Brook University</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Gravitational_anomalies" class="mw-redirect" title="Gravitational anomalies">Gravitational anomalies</a><br /><a href="/wiki/String_theory" title="String theory">String theory</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Theoretical_physics" title="Theoretical physics">Theoretical physics</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Daniel_Z._Freedman" title="Daniel Z. Freedman">Daniel Z. Freedman</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Luis Álvarez-Gaumé</b> (born 1955) is a Spanish <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physicist</a> who works on <a href="/wiki/String_theory" title="String theory">string theory</a> and quantum gravity. </p><p>Luis Álvarez-Gaumé obtained his PhD in 1981 from <a href="/wiki/Stony_Brook_University" title="Stony Brook University">Stony Brook University</a> and worked from 1981 to 1984 at <a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a> as a Junior Fellow, before he moved to <a href="/wiki/Boston_University" title="Boston University">Boston University</a> to work as a professor. From 1986 until 2016, Álvarez-Gaumé was a permanent member of the <a href="/wiki/CERN" title="CERN">CERN</a> Theoretical Physics unit. In 2016, he became the director of the <a href="/wiki/Simons_Center_for_Geometry_and_Physics" title="Simons Center for Geometry and Physics">Simons Center for Geometry and Physics</a> at Stony Brook. </p><p>In the 1980s, Álvarez-Gaumé had various important contributions to the field of string theory and its mathematical framework. Together with <a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a> he showed in 1983 that <a href="/wiki/Quantum_field_theories" class="mw-redirect" title="Quantum field theories">quantum field theories</a> generally have <a href="/wiki/Gravitational_anomaly" title="Gravitational anomaly">gravitational anomalies</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> Shortly after this, <a href="/wiki/Michael_Green_(physicist)" title="Michael Green (physicist)">Michael Green</a> and <a href="/wiki/John_Henry_Schwarz" title="John Henry Schwarz">John Schwarz</a> showed that such anomalies are avoided in various realizations of superstring theory. Álvarez-Gaumé is also known for a physical proof of the <a href="/wiki/Atiyah%E2%80%93Singer_theorem" class="mw-redirect" title="Atiyah–Singer theorem">Atiyah–Singer theorem</a> using <a href="/wiki/Supersymmetry" title="Supersymmetry">supersymmetry</a>. His work spans a range of different subjects, including string perturbation theory at higher orders, quantum field theories on <a href="/wiki/Riemann_surface" title="Riemann surface">Riemann surfaces</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> quantum groups, as well as dualities in string theory and black holes in string theory.<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><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In the 1990s, Álvarez-Gaumé studied supersymmetry breaking at low energies (in <i>N</i> = 2 SUSY <a href="/wiki/Yang%E2%80%93Mills_theory" title="Yang–Mills theory">gauge theories</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><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> He has also co-authored a textbook on <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luis_%C3%81lvarez-Gaum%C3%A9&action=edit&section=1" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFÁlvarez-GauméWitten1984" class="citation journal cs1">Álvarez-Gaumé, Luis; Witten, Edward (1984). "Gravitational Anomalies". <i>Nuclear Physics B</i>. <b>234</b> (2): 269–330. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1984NuPhB.234..269A">1984NuPhB.234..269A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0550-3213%2884%2990066-X">10.1016/0550-3213(84)90066-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nuclear+Physics+B&rft.atitle=Gravitational+Anomalies&rft.volume=234&rft.issue=2&rft.pages=269-330&rft.date=1984&rft_id=info%3Adoi%2F10.1016%2F0550-3213%2884%2990066-X&rft_id=info%3Abibcode%2F1984NuPhB.234..269A&rft.aulast=%C3%81lvarez-Gaum%C3%A9&rft.aufirst=Luis&rft.au=Witten%2C+Edward&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuis+%C3%81lvarez-Gaum%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFÁlvarez-GauméMooreVafa1986" class="citation journal cs1">Álvarez-Gaumé, Luis; Moore, Gregory; <a href="/wiki/Cumrun_Vafa" title="Cumrun Vafa">Vafa, Cumrun</a> (1986). <a rel="nofollow" class="external text" href="http://projecteuclid.org/euclid.cmp/1104115581">"Theta functions, modular invariance and strings"</a>. <i>Communications in Mathematical Physics</i>. <b>106</b> (1): 1–40. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1986CMaPh.106....1A">1986CMaPh.106....1A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01210925">10.1007/BF01210925</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121490383">121490383</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Communications+in+Mathematical+Physics&rft.atitle=Theta+functions%2C+modular+invariance+and+strings&rft.volume=106&rft.issue=1&rft.pages=1-40&rft.date=1986&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121490383%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01210925&rft_id=info%3Abibcode%2F1986CMaPh.106....1A&rft.aulast=%C3%81lvarez-Gaum%C3%A9&rft.aufirst=Luis&rft.au=Moore%2C+Gregory&rft.au=Vafa%2C+Cumrun&rft_id=http%3A%2F%2Fprojecteuclid.org%2Feuclid.cmp%2F1104115581&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuis+%C3%81lvarez-Gaum%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFÁlvarez-GauméGómezVázquez-Mozo2007" class="citation journal cs1">Álvarez-Gaumé, Luis; Gómez, César; Vázquez-Mozo, Miguel A. (2007). "Scaling phenomena in gravity from QCD". <i>Physics Letters B</i>. <b>649</b> (5–6): 478–482. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/0611312">hep-th/0611312</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007PhLB..649..478A">2007PhLB..649..478A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.physletb.2007.04.041">10.1016/j.physletb.2007.04.041</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:14796843">14796843</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Scaling+phenomena+in+gravity+from+QCD&rft.volume=649&rft.issue=5%E2%80%936&rft.pages=478-482&rft.date=2007&rft_id=info%3Aarxiv%2Fhep-th%2F0611312&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A14796843%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.physletb.2007.04.041&rft_id=info%3Abibcode%2F2007PhLB..649..478A&rft.aulast=%C3%81lvarez-Gaum%C3%A9&rft.aufirst=Luis&rft.au=G%C3%B3mez%2C+C%C3%A9sar&rft.au=V%C3%A1zquez-Mozo%2C+Miguel+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuis+%C3%81lvarez-Gaum%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFÁlvarez-Gaumé2009" class="citation journal cs1">Álvarez-Gaumé, Luis (2009). "Scaling Phenomena in gravity and Yang-Mills theories, or black hole formation and its unitarization". <i>Fortschritte der Physik</i>. <b>57</b> (5–7): 327–328. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009ForPh..57..327A">2009ForPh..57..327A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fprop.200900066">10.1002/prop.200900066</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121687991">121687991</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Fortschritte+der+Physik&rft.atitle=Scaling+Phenomena+in+gravity+and+Yang-Mills+theories%2C+or+black+hole+formation+and+its+unitarization&rft.volume=57&rft.issue=5%E2%80%937&rft.pages=327-328&rft.date=2009&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121687991%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1002%2Fprop.200900066&rft_id=info%3Abibcode%2F2009ForPh..57..327A&rft.aulast=%C3%81lvarez-Gaum%C3%A9&rft.aufirst=Luis&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuis+%C3%81lvarez-Gaum%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFÁlvarez-GauméMariñoZamora1998" class="citation journal cs1">Álvarez-Gaumé, Luis; Mariño, Marcos; Zamora, Frederic (1998). "Softly Broken <i>N</i> = 2 QCD with Massive Quark Hypermultiplets, I". <i>International Journal of Modern Physics A</i>. <b>13</b> (3): 403–430. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/9703072">hep-th/9703072</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998IJMPA..13..403A">1998IJMPA..13..403A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2FS0217751X98000184">10.1142/S0217751X98000184</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Modern+Physics+A&rft.atitle=Softly+Broken+N+%3D+2+QCD+with+Massive+Quark+Hypermultiplets%2C+I&rft.volume=13&rft.issue=3&rft.pages=403-430&rft.date=1998&rft_id=info%3Aarxiv%2Fhep-th%2F9703072&rft_id=info%3Adoi%2F10.1142%2FS0217751X98000184&rft_id=info%3Abibcode%2F1998IJMPA..13..403A&rft.aulast=%C3%81lvarez-Gaum%C3%A9&rft.aufirst=Luis&rft.au=Mari%C3%B1o%2C+Marcos&rft.au=Zamora%2C+Frederic&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuis+%C3%81lvarez-Gaum%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFÁlvarez-GauméMariñoZamora1998" class="citation journal cs1">Álvarez-Gaumé, Luis; Mariño, Marcos; Zamora, Frederic (1998). "Softly Broken <i>N</i> = 2 QCD with Massive Quark Hypermultiplets, II". <i>International Journal of Modern Physics A</i>. <b>13</b> (11): 1847–1880. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/9707017">hep-th/9707017</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998IJMPA..13.1847A">1998IJMPA..13.1847A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2FS0217751X98000810">10.1142/S0217751X98000810</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15122485">15122485</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Modern+Physics+A&rft.atitle=Softly+Broken+N+%3D+2+QCD+with+Massive+Quark+Hypermultiplets%2C+II&rft.volume=13&rft.issue=11&rft.pages=1847-1880&rft.date=1998&rft_id=info%3Aarxiv%2Fhep-th%2F9707017&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15122485%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1142%2FS0217751X98000810&rft_id=info%3Abibcode%2F1998IJMPA..13.1847A&rft.aulast=%C3%81lvarez-Gaum%C3%A9&rft.aufirst=Luis&rft.au=Mari%C3%B1o%2C+Marcos&rft.au=Zamora%2C+Frederic&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuis+%C3%81lvarez-Gaum%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFÁlvarez-GauméVázquez-Mozo2012" class="citation book cs1">Álvarez-Gaumé, Luis; Vázquez-Mozo, Miguel (2012). <i>An Invitation to Quantum Field Theory</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-23728-7" title="Special:BookSources/978-3-642-23728-7"><bdi>978-3-642-23728-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Invitation+to+Quantum+Field+Theory&rft.pub=Springer&rft.date=2012&rft.isbn=978-3-642-23728-7&rft.aulast=%C3%81lvarez-Gaum%C3%A9&rft.aufirst=Luis&rft.au=V%C3%A1zquez-Mozo%2C+Miguel&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuis+%C3%81lvarez-Gaum%C3%A9" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luis_%C3%81lvarez-Gaum%C3%A9&action=edit&section=2" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://inspirehep.net/author/profile/L.Alvarez.Gaume.1">Álvarez-Gaumé's profile on INSPIRE-HEP</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": 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