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By D. Zelinsky
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Extra resources for Brauer Groups
7) if M is the number of generators of the subgroup that remains unbroken. 7 Renormalizability and Triangle Anomalies All the techniques for uniﬁed gauge theories have been laid out. The important reason for the attractiveness of spontaneously broken gauge theories for model building is the property of renormalizability. We saw in Chapter 1 that gauge invariance provides a natural explanation for universality of coupling strengths, as is observed in the case of weak interactions. The Higgs–Kibble mechanism provides a way to generate masses of the gauge bosons while at the same time maintaining the freedom to gauge transform the ﬁelds.
The ﬁrst method will be chosen in applying gauge theories to the study of electroweak interactions, whereas the second alternative will be chosen in applications to strong interactions, and this is the focus of this section. Let us brieﬂy discuss the features of strong interactions that suggest its description in terms of a non-abelian gauge theory. The ﬁrst important step in the understanding of nuclear forces was the success of SU(3) symmetry for hadrons, which led Gell-Mann and Zweig to introduce a quark picture of hadrons.
19] D. Gross and R. Jackiw, Phys. Rev. D6, 477 (1972); C. Bouchiat, J. Illiopoulos, and Ph. Meyer, Phys Lett. 38B, 519 (1972). 1 The SU(2)L × U(1) Model of Glashow, Weinberg, and Salam In this section we will apply the ideas of spontaneously broken gauge theories to construct the ﬁrst successful model of the electroweak interaction of quarks and leptons. As we discussed in the Chapter 1 the observed universality of the four-Fermi coupling of weak-decay processes suggests the existence of a hidden symmetry of weak interactions, and the symmetry manifests itself not through the existence of degenerate multiplets but through broken local symmetries.