Quantum Statistical Field Theory in Gravitation and Cosmology

TL;DR

This paper applies quantum open system concepts, especially the closed-time-path formalism, to analyze quantum fields in gravitation and cosmology, revealing fluctuation-dissipation relations and noise effects in semiclassical gravity.

Contribution

It introduces a comprehensive framework using CTP and influence functional formalisms to study quantum field fluctuations, noise, and backreaction in gravitational settings, extending previous approaches.

Findings

Derived influence action for interacting quantum fields.

Established fluctuation-dissipation relations for quantum fields.

Demonstrated noise effects and backreaction in semiclassical gravity.

Abstract

We describe how the concepts of quantum open systems and the methods of closed-time-path (CTP) effective action and influence functional (IF) can be usefully applied to the analysis of statistical mechanical problems involving quantum fields in gravitation and cosmology. In the first lecture we discuss in general terms the relevance of open system concepts in the description of a variety of physical processes, and outline the basics of the CTP and IF formalisms. In the second lecture we illustrate the IF method with a model of two interacting quantum fields, deriving the influence action via a perturbative expansion involving the closed-time-path Green functions. We show how noise of quantum fields can be defined and derive a general fluctuation- dissipation relation for quantum fields. In the third lecture we discuss the problem of backreaction in semiclassical gravity with the example of a scalar field in a Bianchi Type-I universe. We show that the CTP effective action not only yields a real and causal equation of motion with a dissipative term depicting the effect of particle creation, as was found earlier, it also contains a noise term measuring the fluctuations in particle number and governing the metric fluctuations. The particle creation-backreaction problem can be understood as a manifestation of a fluctuation-dissipation relation for quantum fields in dynamic spacetimes, generalizing Sciama's observation for black hole Hawking radiation. A more complete description of semiclassical gravity is given by way of an Einstein-Langevin equation, the conventional theory based on the expectation value of the energy momentum tensor being its