Introduction to Quantum Fields on a Lattice

Clear and pedagogical introduction to quantum fields on a lattice, for advanced undergraduates and graduates.

Jan Smit (Author)

9780521890519, Cambridge University Press

Paperback, published 19 September 2002

284 pages, 74 b/w illus. 1 table 34 exercises
22.9 x 15.2 x 1.7 cm, 0.393 kg

"Recommended." Choice

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.

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.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ]