Smit, J.

2002
Cambridge University Press Cambridge

Abstract: This book provides a concrete introduction to quantum fields on a lattice: a precise and non-perturbative definition of quantum field theory obtained by replacing continuous space-time by a discrete set of points on a lattice. The path integral on the lattice is explained in concrete examples using weak and strong coupling expansions. Fundamental concepts such as 'triviality' of Higgs fields and confinement of quarks and gluons into hadrons are described and illustrated with the results of numerical simulations. The book also provides an introduction to chiral symmetry and chiral gauge theory, as well as quantized non-abelian gauge fields, scaling and universality. Based on the lecture notes of a course given by the author, this book contains many explanatory examples and exercises, and is suitable as a textbook for advanced undergraduate and graduate courses.

Keyword(s): book ; lattice field theory ; path integral ; field theory: scalar ; symmetry: O(N) ; renormalization ; gauge field theory: U(1) ; gauge field theory: SU(N) ; fermion ; critical phenomena ; confinement ; hadron spectroscopy ; symmetry: chiral ; bibliography ; thema EDItEUR::P Mathematics and Science::PH Physics::PHN Nuclear physics ; non-perturbative quantum field theory ; path integrals ; lattice regularisation ; weak and strong coupling expansions ; O(n) models ; gauge field on the lattice ; Higgs field ; quark confinement ; non-Abelian gauge fields ; U(1) gauge theory ; SU(n) gauge theory ; fermions on the lattice ; low mass hadrons in QCD ; chiral symmetry ; temporal gauge quantization ; fermionic coherent states ; spinor fields ; Textbook ; Particle Physics and Nuclear Physics ; Physics and Astronomy ; Theoretical Physics and Mathematical Physics