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Yang–Mills theory
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=== Parallel work on non-Abelian gauge theories === In 1953, in a private correspondence, [[Wolfgang Pauli]] formulated a six-dimensional theory of [[Einstein's field equations]] of [[general relativity]], extending the five-dimensional theory of [[Kaluza–Klein theory|Kaluza, Klein]], [[Vladimir Fock|Fock]], and others to a higher-dimensional internal space.<ref name = Straumann>{{cite arXiv |last=Straumann |first=N. |year=2000 |title=On Pauli's invention of non-abelian Kaluza-Klein Theory in 1953 |eprint=gr-qc/0012054}}</ref> However, there is no evidence that Pauli developed the [[Lagrangian (field theory)|Lagrangian]] of a [[gauge field]] or the quantization of it. Because Pauli found that his theory "leads to some rather unphysical shadow particles", he refrained from publishing his results formally.<ref name=Straumann/> Although Pauli did not publish his six-dimensional theory, he gave two seminar lectures about it in Zürich in November 1953.<ref name = Straumann /> In January 1954 [[Ronald Shaw (physicist)|Ronald Shaw]], a graduate student at the [[University of Cambridge]] also developed a non-Abelian gauge theory for nuclear forces.<ref name=shaw> {{cite journal |last1=Atiyah |first1=M. |authorlink1=Michael Atiyah |date=2017 |title=Ronald Shaw 1929–2016 by Michael Atiyah (1954) |journal=Trinity College Annual Record |volume=2017 |issue= |pages=137–146 |type=memorial |url=https://issuu.com/trinityalumni/docs/trinity_ar_2017_web }} </ref> However, the theory needed massless particles in order to maintain [[gauge invariance]]. Since no such massless particles were known at the time, Shaw and his supervisor [[Abdus Salam]] chose not to publish their work.<ref name=shaw/> Shortly after Yang and Mills published their paper in October 1954, Salam encouraged Shaw to publish his work to mark his contribution. Shaw declined, and instead it only forms a chapter of his PhD thesis published in 1956.<ref> {{cite thesis |last=Shaw |first=Ronald |date=September 1956 |title=The problem of particle types and other contributions to the theory of elementary particles |degree=Ph.D. |at=ch. 3, pp. 34–46 |publisher=[[University of Cambridge]] }} </ref><ref> {{cite book |last=Fraser |first=Gordon |date=2008 |title=Cosmic Anger: Abdus Salam – the first Muslim Nobel scientist |place=Oxford, UK |publisher=Oxford University Press |isbn=978-0199208463 |page=117 }} </ref>
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