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Quantum Fields in Curved Space

Book Description

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

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. Conventions and abbreviations
  8. 1. Introduction
  9. 2. Quantum field theory in Minkowski space
    1. 2.1 Scalar field
    2. 2.2 Quantization
    3. 2.3 Energy–momentum
    4. 2.4 Vacuum energy divergence
    5. 2.5 Dirac spinor field
    6. 2.6 Electromagnetic field
    7. 2.7 Green functions
    8. 2.8 Path-integral quantization
  10. 3. Quantum field theory is curved spacetime
    1. 3.1 Spacetime structure
    2. 3.2 Scalar field quantization
    3. 3.3 Meaning of the particle concept: particle detectors
    4. 3.4 Cosmological particle creation: a simple example
    5. 3.5 Adiabatic vacuum
    6. 3.6 Adiabatic expansion of Green functions
    7. 3.7 Conformal vacuum
    8. 3.8 Fields of arbitrary spin in curved spacetime
  11. 4. Flat spacetime examples
    1. 4.1 Cylindrical two-dimensional spacetime
    2. 4.2 Use of Green functions
    3. 4.3 Boundary effects
    4. 4.4 Moving mirrors
    5. 4.5 Quantum field theory in Rindler space
  12. 5. Curved spacetime examples
    1. 5.1 Robertson−Walker spacetimes
    2. 5.2 Static Robertson−Walker spacetimes
    3. 5.3 The Milne universe
    4. 5.4 De Sitter space
    5. 5.5 Classification of conformal vacua
    6. 5.6 Bianchi I spacetimes and perturbation theory
  13. 6. Stress-tensor renormalization
    1. 6.1 The fundamental problem
    2. 6.2 Renormalization in the effective action
    3. 6.3 Conformal anomalies and the massless case
    4. 6.4 Computing the renormalized stress-tensor
    5. 6.5 Other regularization methods
    6. 6.6 Physical significance of the stress-tensor
  14. 7. Applications of renormalization techniques
    1. 7.1 Two-dimensional examples
    2. 7.2 Robertson–Walker models
    3. 7.3 Perturbation calculation of the stress-tensor
    4. 7.4 Cosmological considerations
  15. 8. Quantum black holes
    1. 8.1 Particle creation by a collapsing spherical body
    2. 8.2 Physical aspects of black hole emission
    3. 8.3 Eternal black holes
    4. 8.4 Analysis of the stress-tensor
    5. 8.5 Further developments
  16. 9. Interacting fields
    1. 9.1 Calculation of S-matrix elements
    2. 9.2 Self-interacting scalar field in curved spacetime
    3. 9.3 Particle production due to interaction
    4. 9.4 Other effects of interactions
  17. References
  18. Index