Symmetry Breaking In The Standard Model: A Non-perturbative Outlook (publications Of The Scuola Normale Superiore)

The book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations. The debated empirical meaning of global and local gauge symmetries is clarified. The absence of Goldstone bosons in the Higgs mechanism is non-perturbatively explained by the validity of Gauss laws obeyed by the currents which generate the related global gauge symmetry. The solution of the U(1) problem and the vacuum structure in quantum chromodynamics (QCD) are obtained without recourse to the problematic semiclassical instanton approximation, by rather exploiting the topology of the gauge group. Cover 1 Half Title Page 2 Title Page 4 Copyright Page 5 Contents 6 Introduction 8 Chapter 1 Spontaneous symmetry breakin 15 1.1 Operational and mathematical description of a physical system 15 1.2 Symmetries and symmetry breaking 18 1.3 Infinitely extended systems. Pure phases and symmetry breaking 19 1.4 The Goldstone theorem 24 1.4.1 Examples 29 1.5 Goldstone theorem in relativistic local quantum field theory 33 Chapter 2 Breaking gauge symmetries. Higgs mechanism 38 2.1 Global gauge symmetries 38 2.2 Local gauge symmetries 47 2.3 Local Gauss law 50 2.3.1 Gauss law, locality and gauge fixing 52 2.3.2 Gauss laws in Yang-Mills quantum theories 57 2.4 Higgs mechanism. Standard treatment 61 2.5 Non-perturbative constructive approaches to symmetry breaking 63 2.6 The Elitzur theorem 66 2.7 A non-perturbative argument for the absence of Goldstone bosons 68 2.8 A theorem on the Higgs phenomenon 71 2.9 Gauge symmetries, observables and states 79 Chapter 3 The U(1) problem in QCD 80 3.1 The U(1) problem in QCD 80 3.1.1 The standard solution 82 3.1.2 A non-perturbative approach without instantons 89 3.2 Topology of the gauge group 90 3.2.1 The temporal gauge. The Gauss law and the physical states 90 3.2.2 The topology of the gauge group 93 3.2.3 The topological current 95 3.3 Gauge group topology solves the U(1) problem 97 3.3.1 Fermions and chiral symmetry 97 3.3.2 Solution of the U(1) problem 99 3.4 Gauge group topology and θ vacua 101 3.5 A prototypic model of QCD vacuum structure 107 Index 113 LECTURE NOTES 115 Front Matter ....Pages I-XIII Spontaneous symmetry breaking (Franco Strocchi)....Pages 1-23 Breaking gauge symmetries. Higgs mechanism (Franco Strocchi)....Pages 25-66 The U(1) problem in QCD (Franco Strocchi)....Pages 67-99 Back Matter ....Pages 101-109