Mathematics – Logic
Scientific paper
Jul 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979gregr..10..807f&link_type=abstract
General Relativity and Gravitation, Volume 10, Issue 10, pp.807-824
Mathematics
Logic
71
Cosmological Models
Scientific paper
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 fieldφ whose equation includes the term ξRφ. Diagonalization of thetotal 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 acanonical 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.
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