Quantum fields in nonstatic background: A histories perspective

For a quantum field living on a non - static spacetime no instantaneousHamiltonian is definable, for this generically necessitates a choice ofinequivalent representation of the canonical commutation relations at eachinstant of time. This fact suggests a description in terms of time - dependentHilbert spaces, a concept that fits naturally in a (consistent) historiesframework. Our primary tool for the construction of the quantum theory in acontinuous -time histories format is the recently developed formalism based onthe notion of the history group . This we employ to study a model systeminvolving a 1+1 scalar field in a cavity with moving boundaries. The instantaneous (smeared) Hamiltonian and a decoherence functional are thenrigorously defined so that finite values for the time - averaged particlecreation rate are obtainable through the study of energy histories. We alsoconstruct the Schwinger - Keldysh closed- time - path generating functional asa ``Fourier transform'' of the decoherence functional and evaluate thecorresponding n - point functions.Comment: 27 pages, LATEX; minor changes and corrections; version to appear in JM