REMARKS ON POSITIVE FREQUENCY AND HAMILTONIANS IN EXPANDING UNIVERSES

We examine critically the persistent belief that the physical interpretation of a quantum field theory in curved space-time is to be found by introducing a notion of particles at each time in terms of the exact eigenstates of some energylike operator at that time. It seems that all straightforward implementations of this principle suffer from either ambiguity or failure to produce finite particle densities and renormalizable energy-momentum tensors. Calculations are done for a cosmological model of Bianchi type I, containing a scalar field φ whose equation includes the term ξRφ. Diagonalization of the total energy suggests a certain particle definition, which, however, yields a finite particle creation rate only when ξ=1/6 and the universe is isotropic. Diagonalization of a canonical Hamiltonian is a prescription loose enough to be made consistent with almost any ansatz (including one that does yield physically acceptable expectation values), hence of no theoretical value. An apparently successful naive approach to the isotropic case (for any ξ) is explained as an unconscious first approximation to an adiabatic analysis of the notion of positive frequency. © 1979 Plenum Publishing Corporation.