Methods of contemporary gauge theory / Yuri Makeenko.

Includes bibliographical references (pages 405-410) and index.

Print version record.

Path Integrals -- Operator calculus -- Free propagator -- Euclidean formulation -- Path-ordering of operators -- Feynman disentangling -- Calculation of the Gaussian path integral -- Transition amplitudes -- Propagators in external field -- Second quantization -- Integration over fields -- Grassmann variables -- Perturbation theory -- Schwinger-Dyson equations -- Commutator terms -- Schwinger-Dyson equations (continued) -- Regularization -- Quantum anomalies from path integral -- QED via path integral -- Chiral Ward identity -- Chiral anomaly -- Chiral anomaly (calculation) -- Scale anomaly -- Instantons in quantum mechanics -- Double-well potential -- The instanton solution -- Instanton contribution to path integral -- Symmetry restoration by instantons -- Topological charge and [theta]-vacua -- Lattice Gauge Theories -- Observables in gauge theories -- Gauge invariance -- Phase factors (definition) -- Phase factors (properties) -- Aharonov-Bohm effect -- Gauge fields on a lattice -- Sites, links, plaquettes and all that -- Lattice formulation -- The Haar measure -- Wilson loops -- Strong-coupling expansion -- Area law and confinement -- Asymptotic scaling -- Lattice methods -- Phase transitions -- Mean-field method -- Mean-field method (variational) -- Lattice renormalization group -- Monte Carlo method -- Some Monte Carlo results -- Fermions on a lattice -- Chiral fermions -- Fermion doubling -- Kogut-Susskind fermions -- Wilson fermions -- Quark condensate -- Finite temperatures -- Feynman-Kac formula.

This book introduces the quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, all of which have important contemporary applications. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are pedagogically introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang-Mills theory. The book uses a modern approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory.

English.

eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - Worldwide