Quantum Fields in Nonstatic background: A Histories Perspective

TL;DR

This paper develops a histories-based quantum framework for non-static spacetimes, enabling rigorous definitions of Hamiltonians and particle creation rates for a scalar field with moving boundaries.

Contribution

It introduces a histories perspective using the history group formalism to analyze quantum fields in non-static backgrounds, including moving boundary conditions.

Findings

Defined energy histories and particle creation rates.

Constructed the Schwinger-Keldysh generating functional.

Evaluated n-point functions in the histories framework.

Abstract

For a quantum field living on a non - static spacetime no instantaneous Hamiltonian is definable, for this generically necessitates a choice of inequivalent representation of the canonical commutation relations at each instant of time. This fact suggests a description in terms of time - dependent Hilbert spaces, a concept that fits naturally in a (consistent) histories framework. Our primary tool for the construction of the quantum theory in a continuous -time histories format is the recently developed formalism based on the notion of the history group . This we employ to study a model system involving a 1+1 scalar field in a cavity with moving boundaries. The instantaneous (smeared) Hamiltonian and a decoherence functional are then rigorously defined so that finite values for the time - averaged particle creation rate are obtainable through the study of energy histories. We also construct the Schwinger - Keldysh closed- time - path generating functional as a ``Fourier transform'' of the decoherence functional and evaluate the corresponding n - point functions.