Gauge theories of the electroweak interaction

Abstract

The gauge theories for the strong and electroweak interaction have become the Standard Model of particle physics. They realize in a consistent way the requirements of quantum theory, special relativity, and symmetry principles. For the first time, we have a consistent theory of the fundamental interac tions that allows for precision calculations for many experiments. The Stan dard Model has, up to now, successfully passed all experimental tests. This success establishes the importance of gauge theories, despite the fact that gravity is not included and that the Standard Model is most likely an effec tive theory resulting from the low-energy limit of a more fundamental theory. The aim of this book is to present the basic ideas and concepts, the tech nical tools, and the predictions of the gauge theories for the fundamental constituents of matter and their interactions: Quantum Chromo dynamics for the strong interaction and the Electroweak Standard Model for the uni fied electromagnetic and weak interaction. 1 Phenomenological basis of gauge theories of strong, electromagnetic, and weak interactions -- 1.1 Elementary particles and their interactions -- 1.2 Elements of relativistic quantum field theory -- 1.3 The quark model of hadrons -- 1.4 Basics of the electroweak interaction -- 1.5 The quark-parton model -- 1.6 Higher-order field-theoretical effects in QED -- 1.7 Towards gauge theories of strong and electroweak interactions -- 2 Quantum theory of Yang-Mills fields -- 2.1 Green functions and S-matrix elements -- 2.2 Path-integral representation of quantum field theory -- 2.3 Local gauge invariance -- 2.4 Path-integral formulation of gauge theories -- 2.5 Renormalization of quantum field theories -- 2.6 Renormalization group -- 2.7 Anomalies -- 2.8 Infrared and collinear singularities -- 2.9 Non-perturbative aspects of gauge theories -- 2.10 Lattice approximation of gauge theories -- 3 Quantum Chromodynamics -- 3.1 Asymptotic freedom of QCD -- 3.2 QCD in deep-inelastic scattering -- 3.3 Perturbative Quantum Chromodynamics -- 3.4 Heavy-quark effective theory (HQET) -- 3.5 Light quarks and chiral perturbation theory -- 3.6 Results of lattice approximation of QCD -- 3.7 Quark confinement -- 3.8 A test of QCD: the running of?S -- 4 Gauge theories of the electroweak interaction -- 4.1 Spontaneous symmetry breaking -- 4.2 The Standard Model of the Electroweak Interaction -- 4.3 Simple applications of the Electroweak Standard Model -- 4.4 Quantization of the Electroweak Standard Model -- 4.5 Renormalization of the Electroweak Standard Model -- 4.6 Electroweak radiative corrections -- 5 Extensions of the Standard Model -- 5.1 Grand unified theories (GUTs) -- 5.2 Supersymmetry -- A Appendix -- A.1 Conventions -- A.2 Feynman rules for the Electroweak Standard Model -- General references.