Finite-Temperature Field Theory

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Professor Kapusta develops the basic formalism and theoretical techniques for studying relativistic quantum field theory at high temperature and density. Topics covered include functional integral representation of the partition function, diagrammatic expansions, linear response theory, screening and collective oscillations, equations of state, phase transitions, restoration of spontaneously broken symmetries, the Goldstone theorem, and infrared problems. Specific physical theories treated include QED, QCD, the ...

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Overview

Professor Kapusta develops the basic formalism and theoretical techniques for studying relativistic quantum field theory at high temperature and density. Topics covered include functional integral representation of the partition function, diagrammatic expansions, linear response theory, screening and collective oscillations, equations of state, phase transitions, restoration of spontaneously broken symmetries, the Goldstone theorem, and infrared problems. Specific physical theories treated include QED, QCD, the Weinberg-Salam model, and effective nuclear field theories. Applications to white dwarfs, neutron stars, ultrarelativistic nucleus-nucleus collisions, and the early universe are discussed. Problems are provided at the end of each chapter, and numerous references to the literature are included.

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Editorial Reviews

Booknews
Derived from a course on relativistic many-body theory presented at the University of Minnesota (1984/86), this demanding text provides advanced graduate students and professionals (particle theorists, astrophysicists) with a careful account of the theory presently available to the study of matter under extreme conditions of energy and density. Ten chapters (with bibliographic notes and exercises), attractively typeset, printed and bound. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780521449458
  • Publisher: Cambridge University Press
  • Publication date: 1/28/1994
  • Series: Monographs on Mathematical Physics Series
  • Edition description: Older Edition
  • Pages: 219
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.67 (d)

Table of Contents

Preface ix
Preface to the Paperback Edition xi
1 Review of quantum statistical mechanics 1
1.1 Ensembles 1
1.2 One bosonic degree of freedom 2
1.3 One fermionic degree of freedom 4
1.4 Noninteracting particles in a box 5
1.5 Bibliography 8
1.6 Exercises 8
2 Functional integral representation of the partition function 9
2.1 Transition amplitude for bosons 9
2.2 Partition function for bosons 12
2.3 Neutral scalar field 13
2.4 Bose-Einstein condensation 16
2.5 Fermions 21
2.6 Remarks on functional integrals 28
2.7 Bibliography 29
2.8 Exercises 30
3 Interactions and diagrammatic techniques 31
3.1 Perturbative expansion 31
3.2 Diagrammatic rules for <[lambda phis superscript 4]> theory 32
3.3 Propagator 36
3.4 First-order corrections to H and ln Z 39
3.5 Summation of infrared divergences 44
3.6 Yukawa theory 46
3.7 Remarks on real-time perturbation theory 50
3.8 Bibliography 52
3.9 Exercises 52
4 Renormalization 54
4.1 Renormalizing <[lambda phis superscript 4]> theory 54
4.2 Renormalization group 55
4.3 Application to the partition function 59
4.4 Bibliography 59
4.5 Exercises 60
5 Quantum electrodynamics 61
5.1 Quantizing the electromagnetic field 61
5.2 Blackbody radiation 65
5.3 Diagrammatic expansions 68
5.4 Photon self-energy 69
5.5 Loop corrections to In Z 72
5.5.1 Two loops 72
5.5.2 Ring diagrams 75
5.5.3 Three loops 78
5.6 White dwarf stars 80
5.7 Bibliography 82
5.8 Exercises 82
6 Linear response theory 84
6.1 Linear response to an external field 84
6.2 Screening of static electric fields 87
6.3 Exact formula for screening length in QED 91
6.4 Plasma oscillations 94
6.5 Bibliography 99
6.6 Exercises 100
7 Spontaneous symmetry breaking and restoration 101
7.1 Charged scalar field with negative mass-squared 101
7.2 Goldstone's theorem 107
7.3 Loop corrections 109
7.4 Higgs model 115
7.5 Bibliography 118
7.6 Exercises 118
8 Quantum chromodynamics 120
8.1 Quarks and gluons 121
8.2 Asymptotic freedom 125
8.3 Perturbative evaluation of partition function 131
8.4 Instantons 135
8.5 Gluon propagator and linear response 140
8.6 Infrared problems 145
8.7 Deconfinement phase transition 147
8.8 Ultrarelativistic nucleus-nucleus collisions 159
8.9 Strange quark matter 165
8.10 Bibliography 168
8.11 Exercises 169
9 Weak interactions 171
9.1 Weinberg-Salam model 171
9.2 Symmetry restoration 175
9.3 Early universe 179
9.4 Bibliography 180
9.5 Exercises 181
10 Nuclear matter 182
10.1 Effective nuclear field theories 182
10.2 Dense nuclear matter 185
10.3 Liquid-gas phase transition 190
10.4 Pion problem 193
10.5 Neutron stars 198
10.6 Bibliography 202
10.7 Exercises 202
Conclusion 204
Appendix 206
A.1 Thermodynamic relations 206
A.2 High-temperature expansion 207
A.3 Microcanonical and canonical ensembles 209
References 213
Index 217
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