You are previewing Quantum Field Theory in Curved Spacetime.
O'Reilly logo
Quantum Field Theory in Curved Spacetime

Book Description

Quantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. Acknowledgments
  8. Conventions and notation
  9. 1. Quantum fields in Minkowski spacetime
    1. 1.1 Canonical formulation
    2. 1.2 Particles
    3. 1.3 Vacuum energy
    4. 1.4 Charged scalar field
    5. 1.5 Dirac field
    6. 1.6 Angular momentum and spin
  10. 2. Basics of quantum fields in curved spacetimes
    1. 2.1 Canonical quantization and conservation laws
    2. 2.2 Scalar field
    3. 2.3 Cosmological model: Arbitrary asymptotically static time dependence
    4. 2.4 Particle creation in a dynamic universe
    5. 2.5 Statistics from dynamics: Spin-0
    6. 2.6 Conformally invariant non-interacting field
    7. 2.7 Probability distribution of created particles
    8. 2.8 Exact solution with particle creation
    9. 2.9 High-frequency blackbody distribution
    10. 2.10 de Sitter spacetime
    11. 2.11 Quantum fluctuations and early inflation
    12. 2.12 Quantizing the inflaton field perturbations
    13. 2.13 A word on interacting quantized fields and on algebraic quantum field theory in curved spacetime
    14. 2.14 Accelerated detector in Minkowski spacetime
  11. 3. Expectation values quadratic in fields
    1. 3.1 Adiabatic subtraction and physical quantities
    2. 3.2 Energy-momentum tensor from trace anomaly
    3. 3.3 Renormalization in general spacetimes
    4. 3.4 Gaussian approximation to propagator
    5. 3.5 Approximate energy-momentum tensor in Schwarzschild, de Sitter, and other static Einstein spacetimes
    6. 3.6 R-summed form of propagator
    7. 3.7 R-summed action and cosmic acceleration
    8. 3.8 Normal coordinate momentum space
    9. 3.9 Chiral current anomaly caused by spacetime curvature
  12. 4. Particle creation by black holes
    1. 4.1 Introduction
    2. 4.2 Classical considerations
    3. 4.3 Quantum aspects
    4. 4.4 Energy-momentum tensor with Hawking flux
    5. 4.5 Back reaction to black hole evaporation
    6. 4.6 Trans-Planckian physics in Hawking radiation and cosmology
    7. 4.7 Further topics: Closed timelike curves; closed-time-path integral
  13. 5. The one-loop effective action
    1. 5.1 Introduction
    2. 5.2 Preliminary definition of the effective action
    3. 5.3 Regularization of the effective action
    4. 5.4 Effective action for scalar fields: Some examples
    5. 5.5 The conformal anomaly and the functional integral
    6. 5.6 Spinors in curved spacetime
    7. 5.7 The effective action for spinor fields
    8. 5.8 Application of the effective action for spinor fields
    9. 5.9 The axial, or chiral, anomaly
  14. 6. The effective action: Non-gauge theories
    1. 6.1 Introduction
    2. 6.2 The Schwinger action principle
    3. 6.3 The Feynman path integral
    4. 6.4 The effective action
    5. 6.5 The geometrical effective action
    6. 6.6 Perturbative expansion of the effective action
    7. 6.7 Renormalization of an interacting scalar field theory
    8. 6.8 The renormalization group and the effective action
    9. 6.9 The effective potential
    10. 6.10 The renormalization of the non-linear sigma model
    11. 6.11 Formal properties of the effective action
    12. Appendix
  15. 7. The effective action: Gauge theories
    1. 7.1 Introduction
    2. 7.2 Gauge transformations
    3. 7.3 The orbit space and the gauge condition
    4. 7.4 Field space reparameterization and the Killing equation
    5. 7.5 The connection and its consequences
    6. 7.6 The functional measure for gauge theories
    7. 7.7 Gauge-invariant effective action
    8. 7.8 Yang–Mills theory, concluded
    9. 7.9 Scalar quantum electrodynamics
    10. Appendix
  16. Appendix: Quantized Inflaton Perturbations
  17. References
  18. Index