Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Overview: Main Themes. Key Issues. Reader’s Guide
- Part I Effective Action and Regularization, Stress Tensor and Fluctuations
- 2 ‘In-Out’ Effective Action. Dimensional Regularization
- 3 ‘In-In’ Effective Action. Stress Tensor. Thermal Fields
- 4 Stress-Energy Tensor and Correlators: Zeta-Function Method
- 5 Stress-Energy Tensor and Correlation. Point Separation
- Part II Infrared Behavior, 2PI, I/N, Backreaction and Semiclassical Gravity
- Part III Stochastic Gravity
- Part IV Cosmological and Black Hole Backreaction with Fluctuations
- Part V Quantum Curvature Fluctuations in de Sitter Spacetime
- References
- Index
2 - ‘In-Out’ Effective Action. Dimensional Regularization
from Part I - Effective Action and Regularization, Stress Tensor and Fluctuations
Published online by Cambridge University Press: 20 January 2020
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Overview: Main Themes. Key Issues. Reader’s Guide
- Part I Effective Action and Regularization, Stress Tensor and Fluctuations
- 2 ‘In-Out’ Effective Action. Dimensional Regularization
- 3 ‘In-In’ Effective Action. Stress Tensor. Thermal Fields
- 4 Stress-Energy Tensor and Correlators: Zeta-Function Method
- 5 Stress-Energy Tensor and Correlation. Point Separation
- Part II Infrared Behavior, 2PI, I/N, Backreaction and Semiclassical Gravity
- Part III Stochastic Gravity
- Part IV Cosmological and Black Hole Backreaction with Fluctuations
- Part V Quantum Curvature Fluctuations in de Sitter Spacetime
- References
- Index
Summary
This chapter presents the familiar Schwinger–DeWitt effective action in the ‘in-out’ formalism, suitable for the computation of S-matrix scattering or transition amplitudes. The effective action method is well suited to the treatment of backreaction problems for quantum processes in dynamical background spacetimes, as it yields equations of motion for both the quantum field and the spacetime in a self-consistent way. In the second part, after a quick refresh of basic field theory and quantum fields in curved spacetime, we construct the ‘in-out’ effective action of an interacting quantum field and apply it to the effects of particle creation and interaction in the Friedmann–Lemaitre–Robertson–Walker universe. We illustrate how dimensional regularization is implemented. The third part treats the case where changes in the background spacetime and fields are gradual enough that one can perform a derivative expansion beyond the constant background, introduce momentum space representation for the propagators and obtain a quasi-local effective action in a closed form. The fourth part discusses dimensional regularization and the derivation of renormalization group equations, using the Phi-4 theory as an example.
Keywords
- Type
- Chapter
- Information
- Semiclassical and Stochastic GravityQuantum Field Effects on Curved Spacetime, pp. 37 - 78Publisher: Cambridge University PressPrint publication year: 2020