Book contents
- Frontmatter
- Contents
- List of exercises
- List of projects
- Preface
- How to use this book
- 1 Special relativity
- 2 Scalar and electromagnetic fields in special relativity
- 3 Gravity and spacetime geometry: the inescapable connection
- 4 Metric tensor, geodesics and covariant derivative
- 5 Curvature of spacetime
- 6 Einstein's field equations and gravitational dynamics
- 7 Spherically symmetric geometry
- 8 Black holes
- 9 Gravitational waves
- 10 Relativistic cosmology
- 11 Differential forms and exterior calculus
- 12 Hamiltonian structure of general relativity
- 13 Evolution of cosmological perturbations
- 14 Quantum field theory in curved spacetime
- 15 Gravity in higher and lower dimensions
- 16 Gravity as an emergent phenomenon
- Notes
- Index
14 - Quantum field theory in curved spacetime
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- List of exercises
- List of projects
- Preface
- How to use this book
- 1 Special relativity
- 2 Scalar and electromagnetic fields in special relativity
- 3 Gravity and spacetime geometry: the inescapable connection
- 4 Metric tensor, geodesics and covariant derivative
- 5 Curvature of spacetime
- 6 Einstein's field equations and gravitational dynamics
- 7 Spherically symmetric geometry
- 8 Black holes
- 9 Gravitational waves
- 10 Relativistic cosmology
- 11 Differential forms and exterior calculus
- 12 Hamiltonian structure of general relativity
- 13 Evolution of cosmological perturbations
- 14 Quantum field theory in curved spacetime
- 15 Gravity in higher and lower dimensions
- 16 Gravity as an emergent phenomenon
- Notes
- Index
Summary
Introduction
This chapter describes some interesting results that arise when one studies standard quantum field theory in a background spacetime with a nontrivial metric. It turns out that the quantum field theory in a curved spacetime (or a non-inertial coordinate system) with a horizon exhibits some peculiar and universal properties. In particular, the study of the quantum field suggests that the horizon is endowed with a temperature T = k/2π (in natural units with ħ = c = kB = 1), where k is the surface gravity of the horizon. This result can be viewed from very different perspectives, not all of which can be proved to be rigorously equivalent to one another. In view of the importance of this result, most of this chapter will concentrate on obtaining this result using different techniques and interpreting it physically. The latter part of the chapter will develop quantum field theory in an external Friedmann universe and will apply that formalism to study the generation of perturbations during the inflationary phase of the universe.
Review of some key results in quantum field theory
Fortunately, most of the important results we are interested in can be obtained with a minimum amount of background knowledge in quantum field theory. In order to set the stage, we shall rapidly review the necessary concepts in this section.
Quantum field theory attempts to describe particles as excitations of an underlying field.
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- Information
- GravitationFoundations and Frontiers, pp. 591 - 642Publisher: Cambridge University PressPrint publication year: 2010