Methods of contemporary gauge theory /
Makeenko, Yuri, 1951-
Methods of contemporary gauge theory / Yuri Makeenko. - New York : Cambridge University Press, 2002. - 1 online resource (xii, 417 pages) : illustrations - Cambridge monographs on mathematical physics . - Cambridge monographs on mathematical physics. .
Includes bibliographical references (pages 405-410) and index.
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.
0511064012 (electronic bk.) 9780511064012 (electronic bk.) 9780511535147 (electronic bk.) 0511535147 (electronic bk.) 1280415193 9781280415197 0511057687 9780511057687 0511072473 9780511072475 1107131804 9781107131804 9786610415199 6610415196 1139147544 9781139147545 0511169981 9780511169984 0511331223 9780511331220
Gauge fields (Physics)
Mathematical physics.
Champs de jauge (Physique)
Physique mathématique.
SCIENCE--Waves & Wave Mechanics.
Gauge fields (Physics)
Mathematical physics.
Eichtheorie
Quantentheorie
Kwantumveldentheorie.
Invarianten.
Electronic books.
Electronic books.
QC793.3.G38 / M35 2002eb
530.14/35
Methods of contemporary gauge theory / Yuri Makeenko. - New York : Cambridge University Press, 2002. - 1 online resource (xii, 417 pages) : illustrations - Cambridge monographs on mathematical physics . - Cambridge monographs on mathematical physics. .
Includes bibliographical references (pages 405-410) and index.
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.
0511064012 (electronic bk.) 9780511064012 (electronic bk.) 9780511535147 (electronic bk.) 0511535147 (electronic bk.) 1280415193 9781280415197 0511057687 9780511057687 0511072473 9780511072475 1107131804 9781107131804 9786610415199 6610415196 1139147544 9781139147545 0511169981 9780511169984 0511331223 9780511331220
Gauge fields (Physics)
Mathematical physics.
Champs de jauge (Physique)
Physique mathématique.
SCIENCE--Waves & Wave Mechanics.
Gauge fields (Physics)
Mathematical physics.
Eichtheorie
Quantentheorie
Kwantumveldentheorie.
Invarianten.
Electronic books.
Electronic books.
QC793.3.G38 / M35 2002eb
530.14/35