Quarks, Gluons and Lattices

Michael Creutz

doi:10.1017/9781009290395

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.

'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

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

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Contents

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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Quarks, Gluons and Lattices

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