Introduction to Quantum Fields on a Lattice

by Jan Smit

Overview

This book provides a concise 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. Originally published in 2002, this title has been reissued as an Open Access publication on Cambridge Core.

Product Details

ISBN-13:	9781009402750
Publisher:	Cambridge University Press
Publication date:	07/27/2023
Series:	Cambridge Lecture Notes in Physics
Pages:	284
Product dimensions:	5.94(w) x 8.98(h) x 0.59(d)

Table of Contents

Preface; 1. Introduction; 2. Path integral and lattice regularisation; 3. O(n) models; 4. Gauge field on the lattice; 5. U(1) and SU(n) gauge theory; 6. Fermions on the lattice; 7. Low mass hadrons in QCD; 8. Chiral symmetry; Appendix 1. SU(n); Appendix 2. Temporal gauge quantization in the continuum; Appendix 3. Fermionic coherent states; Appendix 4. Spinor fields.

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