Quantum Fields on a Lattice

István Montvay and Gernot Münster

Webpage of the book at Cambridge University Press

Description

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.

Contents

1. Preface
2. Introduction
   • Historical remarks
   • Path integral in quantum mechanics
   • Euclidean quantum field theory
   • Euclidean functional integrals
   • Quantum field theory on a lattice
   • Continuum limit and critical behaviour
   • Renormalization group equations
   • Thermodynamics of quantum fields
3. Scalar fields
   • phi-4 model on the lattice
   • Perturbation theory
   • Hopping parameter expansions
   • Lüscher-Weisz solution and triviality of the continuum limit
   • Finite-volume effects
   • N-component model
4. Gauge fields
   • Continuum gauge fields
   • Lattice gauge fields and Wilson's action
   • Perturbation theory
   • Strong-coupling expansion
   • Static quark potential
   • Glueball spectrum
   • Phase structure of lattice gauge theory
5. Fermion fields
   • Fermionic variables
   • Wilson fermions
   • Kogut-Susskind staggered fermions
   • Nielsen-Ninomiya theorem and mirror fermions
   • QED on the lattice
6. Quantum chromodynamics
   • Lattice action and continuum limit
   • Hadron spectrum
   • Broken chiral symmetry on the lattice
   • Hadron thermodynamics
7. Higgs and Yukawa models
   • Lattice Higgs models
   • Lattice Yukawa models
8. Simulation algorithms
   • Numerical simulation and Markov processes
   • Metropolis algorithms
   • Heatbath algorithms
   • Fermions in numerical simulations
   • Fermion algorithms based on differential equations
   • Hybrid Monte Carlo algorithms
   • Cluster algorithms
9. Appendix
10. References
11. Index