Quantum Fields in Non-Static Background: A Histories Perspective

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 closedtime path generating functional as a “Fourier transform” of the decoherence functional and evaluate the corresponding n point functions. E-mail:[email protected]