Quantum Fields in Curved Space

by N. D. Birrell , P. C. W. Davies

• ISBN13: 9780521233859
• ISBN10: 0521233852
• Format: Hardcover
• Copyright: 1982-04-30
• Publisher: Cambridge University Press

Summary

This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

Table of Contents

Preface	p. vii
Conventions and abbreviations	p. ix
Introduction	p. 1
Quantum field theory in Minkowski space	p. 10
Scalar field	p. 10
Quantization	p. 12
Energy-momentum	p. 14
Vacuum energy divergence	p. 15
Dirac spinor field	p. 17
Electromagnetic field	p. 19
Green functions	p. 20
Path-integral quantization	p. 28
Quantum field theory in curved spacetime	p. 36
Spacetime structure	p. 37
Scalar field quantization	p. 43
Meaning of the particle concept: particle detectors	p. 48
Cosmological particle creation: a simple example	p. 59
Adiabatic vacuum	p. 62
Adiabatic expansion of Green functions	p. 73
Conformal vacuum	p. 79
Fields of arbitrary spin in curved spacetime	p. 81
Flat spacetime examples	p. 89
Cylindrical two-dimensional spacetime	p. 90
Use of Green functions	p. 94
Boundary effects	p. 96
Moving mirrors	p. 102
Quantum field theory in Rindler space	p. 109
Curved spacetime examples	p. 118
Robertson-Walker spacetimes	p. 119
Static Robertson-Walker spacetimes	p. 122
The Milne universe	p. 124
De Sitter space	p. 129
Classification of conformal vacua	p. 138
Bianchi I spacetimes and perturbation theory	p. 142
Stress-tensor renormalization	p. 150
The fundamental problem	p. 151
Renormalization in the effective action	p. 159
Conformal anomalies and the massless case	p. 173
Computing the renormalized stress-tensor	p. 189
Other regularization methods	p. 206
Physical significance of the stress-tensor	p. 214
Applications of renormalization techniques	p. 225
Two-dimensional examples	p. 225
Robertson-Walker models	p. 232
Perturbation calculation of the stress-tensor	p. 237
Cosmological considerations	p. 243
Quantum black holes	p. 249
Particle creation by a collapsing spherical body	p. 250
Physical aspects of black hole emission	p. 264
Eternal black holes	p. 275
Analysis of the stress-tensor	p. 283
Further developments	p. 287
Interacting fields	p. 292
Calculation of S-matrix elements	p. 292
Self-interacting scalar field in curved spacetime	p. 301
Particle production due to interaction	p. 314
Other effects of interactions	p. 317
References	p. 323
Index	p. 337
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