Introduction to Quantum Fields on a Lattice

Jan Smit

doi:10.1017/9781009402705

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This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Jiang, Yunfeng 2023. TT¯ Deformation: A Lattice Approach. Symmetry, Vol. 15, Issue. 12, p. 2212.

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Wang, L. Aarts, G. and Zhou, K. 2024. Diffusion models as stochastic quantization in lattice field theory. Journal of High Energy Physics, Vol. 2024, Issue. 5,

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Smit, Jan 2024. Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations. Physical Review D, Vol. 110, Issue. 12,

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Jan Smit, Universiteit van Amsterdam

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:: 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

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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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Introduction to Quantum Fields on a Lattice

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xii

1 - Introduction
pp 1-7

2 - Path-integral and lattice regularization
pp 8-31

3 - O(n) models
pp 32-82

4 - Gauge field on the lattice
pp 83-114

5 - U(1)and SU(n) gauge theory
pp 115-148

6 - Fermions on the lattice
pp 149-169

7 - Low-mass hadrons in QCD
pp 170-192

8 - Chiral symmetry
pp 193-228

Appendix A - SU(n)
pp 229-238

Appendix B - Quantization in the temporal gauge
pp 239-241

Appendix C - Fermionic coherent states
pp 242-252

Appendix D - Spinor fields
pp 253-257

Notes
pp 258-260

References
pp 261-266

Index
pp 267-272

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Introduction to Quantum Fields on a Lattice

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