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Gauge theory of the strong and electroweak interaction. 3rd revised ed. (English) Zbl 0991.81001
Leipzig: Teubner. xi, 784 p. (2001).
The first edition published in 1981 and the second ed. in 1983 were not reviewed.
In this third ed. of the textbook, a comprehensive summary of gauge theories (GT) of the fundamental interactions of elementary particles is given. In the beginning, the main elements of the relativistic quantum theory (QFT) are briefly reviewed. Then the basic ideas and concepts, the technical tools and the predictions of the quantum chromodynamics (QCD) for strong interaction and the electroweak standard model (EWSM) for the unified electromagnetic and weak interactions are presented and discussed in detail. Particularly, the intimate connection between the basic experimental facts, including the latest results, and the formulation (actual status) of the QCD and EWSM is outlined.
The book is organized as follows:
Part 1. Phenomenological basis of gauge theories of strong, electromagnetic and weak interactions, (pp. 1-84; 61 references). Elementary particles and their interactions (lepton and quarks, fundamental interactions). Elements of relativistic QFT (basic concepts, Lie algebras and Lie groups, conserved currents and charges). The quark model of hadrons (quantum numbers and wave functions of hadrons, colors, quark dynamics – quarkonia). Basics of electroweak interaction. The quark-parton model (scaling in deep-inelastic lepton-nucleon scattering, the parton model, applications and universality). Higher order field-theoretical effects in quantum electrodynamics, QED (QED and QFT, a test of QED: magnetic moment of muon). Towards gauge theories of strong and electroweak interactions.
Part 2. Quantum theory of Yang-Mills fields. (pp. 85-425; 244 ref.), Green functions and \(S\)-matrix elements (principles of QFT, Green functions, \(S\)-matrix and LSZ (Lehmann-Symanzik-Zimmermann formula, connected Green function and vertex functions, scattering of composite particles). Path-integral representation of QFT (functional calculus, generating functionals of Green functions, functional-integral representation of \(S\)-matrix, the field-theoretical path-integral, Feynman rules, Ward identities, equations of motion for Green functions). Local gauge invariance (QED, geometry of non-abelian gauge symmetry, Yang-Mills field theories). Path-integral formulation of GT (path-integral quantization of GT, Feynman rules, BRS (Becchi-Rouet-Stora) invariance and Slavnov-Taylor identities, background field method).
Renormalization of QFT (divergences, one-loop corrections, one-loop renormalization of GT, proof of renormalizability). Renormalization group, RG (RG equation, RG function and anomalous dimensions of massless GT, relation between different renormalization schemes, running unrenormalized coupling constant). Anomalies (triangle-graph anomaly, anomalies in GT). Infrared and collinear singularities (origin of mass singularities, infrared singularities, collinear singularities in QED). Non-perturbative aspects of GT (topological quantum numbers, index theorem, path-integral and topology). Lattice approximation of GT (basics, strong-coupling approximation, numerical methods, transition to continuum, finite-size effects; lattice approximation of fermionic interactions).
Part 3. Quantum chromodynamics (pp. 426-565; 198 ref). Asymptotic freedom of QCD (running coupling constant, higher-order corrections, running quark masses). QCD in deep-inelastic scattering (field-theoretical approach and QCD corrections to parton model, evolution equations, experimental tests of QCD). Perturbative QCD (one-loop-corrections to parton model, factorization and operator-product expansion, lepton pair productions in hadron-hadron scattering, jet and total hadronic cross sections). Heavy-quark effective theory (Lagrangian, symmetries, applications). Light quarks and chiral perturbation theory (chiral symmetry of massless QCD, pion-pole dominance and effective low-energy theory, nonlinear sigma-model, breaking of chiral invariance, applications of chiral perturbation theory). Results of lattice approximation of QCD (hadron spectrum, glueballs, connection between long- and short-distance physics: nonperturbative renormalization group). Quark confinement (Wilson criterion, quark confinement in strong-coupling approximation, string picture, long-range correlations of QCD vacuum). A test of QCD: running coupling constant \(\alpha_s\).
Part 4. Gauge theories of the electroweak interactions, (pp. 566-715; 138 ref.). Spontaneous symmetry breaking (spontaneous breaking of global a local symmetries). The standard model of electroweak interactions (Lagrangian of EWSM, Lagrangian in physical bases). Simple applications of the EWSM \((W\)-pair production in \(e^+e^-\)-annihilation, production and decay of Higgs boson). Quantization of the EWSM (gauge fixing and Faddeev-Popov rule, BKS symmetry and physical fields, Slavnov-Taylor and Lie identities, background-field method for EWSM, charge universality, Goldstone-boson equivalence theorem). Renormalization of the EWSM (renormalization transformation in on-shell scheme, renormalization conditions, explicit form of renormalization constants, renormalization within background-field method, mass renormalization for unstable particles). Electroweak radiative corrections (fermionic contributions to gauge boson self-energies, parameter relations in higher orders, decay widths of weak gauge bosons, \(Z\)-boson physics, precision tests of electroweak interactions, status of EWSM and perspectives).
Part 5. Extensions of the standard model (pp. 716-741; 9 ref.). Grand unified theories, GUTs (unification of coupling constants, proton decay, hierarchy (fine-tuning) problem, SU(5) GUT). Supersymmetry (supersymmetry algebra, chiral multiplet and Wess-Zumino model, improved ultraviolet properties of supersymmetric theories, minimal supersymmetric standard model, supersymmetric grand unification).
Appendix: Conventions. Feynman rules for the EWSM.
General references: Elementary particle physics (4). Electroweak interactions (3). Field theory (7). Glashow-Salam-Weinberg theory (3). Group theory (4). General unified theories (2). Quantum electrodynamics (3). Statistical mechanics (3). Supersymmetry (4). Lattice gauge theory (3).
The textbook is addressed to graduate students of physics as well as to scientists who work or are interested in high energy physics.
Reviewer: A.A.Bogush (Minsk)

81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
81T13 Yang-Mills and other gauge theories in quantum field theory
00A79 Physics
81V05 Strong interaction, including quantum chromodynamics
81V10 Electromagnetic interaction; quantum electrodynamics
81V15 Weak interaction in quantum theory
81V22 Unified quantum theories