Gauge Fields: An Introduction To Quantum Theory, Second Edition (frontiers In Physics)

Gauge field theory describes the physics of elementary particles adequately at moderate energies. Besides, the methods applied in the field theory of relativistic strings represent a direct generalization of the methods of gauge field theory, to which this book is devoted. For this reason the author considers a new edition of it to be useful, both for direct applications of the already developed gauge theory and for search of new ways. Content: Cover Title Page Copyright Page Frontiers in Physics EDITORâ#x80 #x99 S FOREWORD PREFACE TO THE SECOND REVISED (RUSSIAN) EDITION PREFACE TO THE ORIGINAL (RUSSIAN) EDITION Table of Contents 1: INTRODUCTION: FUNDAMENTALS OF CLASSICAL GAUGE FIELD THEORY 1.1 Basic Concepts and Notation 1.2 Geometrical Interpretation of the Yang-Mills Field 1.3 Dynamical Models With Gauge Fields 2: QUANTUM THEORY IN TERMS OF PATH INTEGRALS 2.1 The Path Integral Over Phase Space 2.2 The Path Integral in the Holomorphic Representation 2.3 The Generating functional for the S-matrix in field theory. 2.4 The S-Matrix as a Functional on Classical Solutions2.5 The Path Integral Over Fermi Fields 2.6 The Properties of the Path Integral in Perturbation Theory 3: QUANTIZATION OF THE YANG-MILLS FIELD 3.1 The Lagrangian of the Yang-Mills Field and the Specific Properties of Its Quantization 3.2 The Hamiltonian Formulation of the Yang-Mills Field and Its Quantization 3.3 Covariant Quantization Rules and the Feynman Diagram Technique 3.4 Interaction with Fields of Matter 4: RENORMALIZATION OF GAUGE THEORIES 4.1 Examples of the Simplest Diagrams 4.2 The R-Operation and Counterterms. 4.3 Invariant Regularizations: The Pauli-Villars Procedure4.4 The Method of Higher Covariant Derivatives 4.5 Dimensional Regularization 4.6 Gauge Fields in Lattice Space-Time 4.7 Generalized Ward Identities 4.8 The Structure of the Renormalized Action 4.9 The Renormalized S-Matrix 4.10 The S-Matrix in the Covariant Formalism 4.11 Anomalous Ward Identities 5: SOME APPLICATIONS AND CONCLUSION 5.1 Unified Models of Weak and Electromagnetic Interactions 5.2 Asymptotic Freedom. Gauge Theories of Strong Interactions BIBLIOGRAPHY NOTES. SUPPLEMENT IN PROOF: ANOMALOUS COMMUTATOR OF THE GAUSS LAWREFERENCES NOTATION. This book focuses on the methods applied in the field theory of relativistic strings, which represent a direct generalization of the methods of gauge field theory. It deals with the geometrical aspects of the gauge field theory and illuminates the quantum theory of the Yang-Mills fields. The theory of gauge fields at present represents the widely accepted theoretical basis of elementary particle physics.