Quantum Fields on a Lattice

István Montvay and Gernot Münster

Cambridge Monographs on Mathematical Physics
Cambridge University Press 1994
505 pages, 100 line diagrams
Hardback, ISBN 0-521-40432-0 (out of print)
Paperback, ISBN 0-521-59917-2

Webpage of the book at Cambridge University Press


This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and the electroweak interactions of elementary particles.

Quantum field theory describes basic physical phenomena over an extremely wide range of length or energy scales. Quantum fields exist in space and time, which can be approximated by a set of lattice points. This approximation allows the application of powerful analytical and numerical techniques, and has provided a powerful tool for the study of both the strong and the electroweak interaction. After introductory chapters on scalar fields, gauge fields and fermion fields, the book studies quarks and gluons in QCD and fermions and bosons in the electroweak theory. The last chapter is devoted to numerical simulation algorithms which have been used in recent large-scale numerical simulations.

This book will be valuable for graduate students and researchers in theoretical physics, elementary particle physics, and field theory, interested in non-perturbative approximations and numerical simulations of quantum field phenomena.


  1. Preface
  2. Introduction
  3. Scalar fields
  4. Gauge fields
  5. Fermion fields
  6. Quantum chromodynamics
  7. Higgs and Yukawa models
  8. Simulation algorithms
  9. Appendix
  10. References
  11. Index