Methods of Contemporary Gauge Theory
This 2002 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 an 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.
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1/N-expansion Abelian analogous associated asymptotic boundary conditions calculation chiral classical commutator continuum limit contour d-dimensional deﬁned denotes depicted in Fig derivative described dimensions Euclidean expansion fermions Feynman ﬁeld finite formula four-Fermi gauge field gauge group gauge invariant gauge transformation Gaussian given by Eq gluon hadron index lines instantons interaction large-N limit lattice gauge theory lattice regularization Lett loop equation matrix Monte Carlo non-Abelian nonperturbative Nucl obtain open Wilson loops operator parameter partition function path integral perturbation theory phase factor phase transition Phys planar diagrams planar graphs plaquette Polyakov potential Problem propagator quantum field theory quark quark loops quenched Eguchi–Kawai model Remark renormalization representation reproduces RHS of Eq scalar Sect string SU(N Substituting symmetry term twisted Eguchi–Kawai model twisted reduced model unitary vanishes variables vector Wilson loop Wilson loop average Yang–Mills theory