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  3. Introduction to Quantum Fields on a Lattice
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Publisher:
Cambridge University Press
Online publication date:
July 2023
Print publication year:
2023
Online ISBN:
9781009402705
DOI:
https://doi.org/10.1017/9781009402705
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
Subjects:
Particle Physics and Nuclear Physics, Physics and Astronomy, Theoretical Physics and Mathematical Physics
Series:
Cambridge Lecture Notes in Physics
Information

Book description

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.

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Contents

Full book PDF
Contents
  • Frontmatter
    pp i-vi
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  • Contents
    pp vii-x
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  • Preface
    pp xi-xii
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  • 1 - Introduction
    pp 1-7
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  • 2 - Path-integral and lattice regularization
    pp 8-31
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  • 3 - O(n) models
    pp 32-82
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  • 4 - Gauge field on the lattice
    pp 83-114
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  • 5 - U(1)and SU(n) gauge theory
    pp 115-148
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  • 6 - Fermions on the lattice
    pp 149-169
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  • 7 - Low-mass hadrons in QCD
    pp 170-192
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  • 8 - Chiral symmetry
    pp 193-228
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  • Appendix A - SU(n)
    pp 229-238
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  • Appendix B - Quantization in the temporal gauge
    pp 239-241
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  • Appendix C - Fermionic coherent states
    pp 242-252
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  • Appendix D - Spinor fields
    pp 253-257
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  • Notes
    pp 258-260
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  • References
    pp 261-266
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  • Index
    pp 267-272
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