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Publisher:
Cambridge University Press
Online publication date:
November 2022
Print publication year:
2023
Online ISBN:
9781009290395
Creative Commons:
Creative Common License - CC Creative Common License - BY Creative Common License - NC Creative Common License - ND
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0 https://creativecommons.org/creativelicenses

Book description

This book introduces the lattice approach to quantum field theory. The spectacular successes of this technique include compelling evidence that exchange of gauge gluons can confine the quarks within subnuclear matter. The lattice framework enables novel schemes for quantitative calculation and has caused considerable cross-disciplinary activity between elementary particle and solid state physicists. The treatment begins with the lattice definition of a path integral and ends on Monte Carlo simulation methods. Other topics include invariant group integration, duality, mean field theory and renormalization group techniques. The reader is assumed to have a basic background in relativistic quantum mechanics and some exposure to gauge theories.

Reviews

'The purpose of Mike Creutz's elegant book is to provide a gentle introduction to the basic results in lattice field theory. It succeeds admirably. Without drowning the reader in detail, sufficient background is given to make the book very readable and provide an easy route to the research literature. Enough examples of calculation are given to develop real confidence in manipulating gauge groups, group integrals, duality and all the other tools of the trade. I recommend the book in the strongest terms to all interested in the fundamental structure of nature and the surprises quantum field theory has in store.'

Source: Nature

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Contents

Full book PDF
  • Frontmatter
    pp i-iv
  • Contents
    pp v-v
  • Preface
    pp vi-vi
  • 1 - Quarks and gluons
    pp 1-4
  • 2 - Lattices
    pp 5-7
  • 3 - Path integrals and statistical mechanics
    pp 8-13
  • 4 - Scalar fields
    pp 14-19
  • 5 - Fermions
    pp 20-28
  • 6 - Gauge fields
    pp 29-33
  • 7 - Lattice gauge theory
    pp 34-38
  • 8 - Group integration
    pp 39-50
  • 9 - Gauge–invariance and order parameters
    pp 51-59
  • 10 - Strong coupling
    pp 60-76
  • 11 - Weak coupling
    pp 77-80
  • 12 - Renormalization and the continuum limit
    pp 81-87
  • 13 - Asymptotic freedom and dimensional transmutation
    pp 88-93
  • 14 - Mean field theory
    pp 94-100
  • 15 - The Hamiltonian approach
    pp 101-107
  • 16 - Discrete groups and duality
    pp 108-116
  • 17 - Migdal–Kadanoff recursion relations
    pp 117-126
  • 18 - Monte Carlo simulation I: the method
    pp 127-139
  • 19 - Monte Carlo simulation II: measuring observables
    pp 140-150
  • 20 - Beyond the Wilson action
    pp 151-161
  • References
    pp 162-166
  • Index
    pp 167-172

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