Introduction to Renormalization Theory and Chiral Gauge Theories in Dimensional Regularization with Non-Anticommuting γ5

被引:11
作者
Belusca-Maito, Hermes [1 ]
Ilakovac, Amon [1 ]
Kuehler, Paul [2 ]
Mador-Bozinovic, Marija [1 ]
Stoeckinger, Dominik [2 ]
Weisswange, Matthias [2 ]
机构
[1] Univ Zagreb, Dept Phys, Bijenicka Cesta 32, HR-10000 Zagreb, Croatia
[2] Tech Univ Dresden, Inst Kern & Teilchenphys, Zellescher Weg 19, DE-01069 Dresden, Germany
来源
SYMMETRY-BASEL | 2023年 / 15卷 / 03期
关键词
renormalization; chiral gauge theories; dimensional regularization; PERTURBATION LAGRANGIAN THEORY; ELECTROWEAK STANDARD MODEL; WARD-TAKAHASHI IDENTITY; PARAMETER DEPENDENCE; GREENS FUNCTIONS; GROUP EQUATION; REDUCTION; SYMMETRIES; AMPLITUDES; ANOMALIES;
D O I
10.3390/sym15030622
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for ?5. One goal was to show how chiral gauge theories can be renormalized despite the spurious breaking of gauge invariance and how to obtain the required symmetry-restoring counterterms. A second goal was to familiarize the reader with the theoretical basis of the renormalization of chiral gauge theories, the theorems that guarantee the existence of renormalized chiral gauge theories at all orders as consistent quantum theories. Relevant topics include BPHZ renormalization, Slavnov-Taylor identities, the BRST formalism, and algebraic renormalization, as well as the theorems guaranteeing that dimensional regularization is a consistent regularization/renormalization scheme. All of these, including their proofs and interconnections, are explained and discussed in detail. Further, these theoretical concepts are illustrated in practical applications with the example of an Abelian and a non-Abelian chiral gauge theory. Not only the renormalization procedure for such chiral gauge theories is explained step by step, but also the results of all counterterms, including the symmetry-restoring ones, necessary for the consistent renormalization, are explicitly provided.
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页数:113
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