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Concept
Yang–Mills theory
Summary
In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(n), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using these non-abelian Lie groups and is at the core of the unification of the electromagnetic force and weak forces (i.e. U(1) × SU(2)) as well as quantum chromodynamics, the theory of the strong force (based on SU(3)). Thus it forms the basis of our understanding of the Standard Model of particle physics.
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, Fock, and others to a higher-dimensional internal space. However, there is no evidence that Pauli developed the 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. Although Pauli did not publish his six-dimensional theory, he gave two seminar lectures about it in Zürich in November 1953.
Recent research shows that an extended Kaluza–Klein theory is in general not equivalent to Yang–Mills theory, as the former contains additional terms. Chen Ning Yang long considered the idea of non-abelian gauge theories. Only after meeting Robert Mills did he introduce the junior scientist to the idea and lay the key hypothesis that Mills would use to assist in creating a new theory. This eventually became the Yang–Mills theory, as Mills himself discussed:"During the academic year 1953-1954, Yang was a visitor to Brookhaven National Laboratory ... I was at Brookhaven also...and was assigned to the same office as Yang. Yang, who has demonstrated on a number of occasions his generosity to physicists beginning their careers, told me about his idea of generalizing gauge invariance and we discussed it at some length...
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