Quantum Fields in Nonstatic background: A Histories Perspective

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.

27 pages, LATEX; minor changes and corrections; version to appear in JMP

References in corpus (7)

• Stochastic semiclassical cosmological models
• The action operator for continuous-time histories
• Continuous Time and Consistent Histories
• An effective stochastic semiclassical theory for the gravitational field
• Generalized Quantum Theory and Black Hole Evaporation
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Cited by in corpus (7)

• Histories quantisation of parameterised systems: I. Development of a general algorithm
• Quantum processes on phase space
• Poincare' invariance for continuous-time histories
• Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
• Continuous-time histories: observables, probabilities, phase space structure and the classical limit
• A Consistent Histories approach to the Unruh effect
• Classical History Theory of Vector Fields