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A constraint on physical quantum states in cosmological space-times

Authors:	A H Najmi A C Ottewill

Institution:	(1) Department of Physics, University of Utah, 84112 Salt Lake City, Utah;(2) Enrico Fermi Institute, University of Chicago, 5640 S. Ellis Ave., 60637 Chicago, Illinois;(3) Present address: Department of Astrophysics, University of Oxford, South Parks Road, Oxford, South Parks Road, OX1-3RQ Oxford, England

Abstract:	The problem of constructing the Hilbert space of physical states for a free scalar quantum field propagating on a cosmological background is considered. The concept of energy-momentum for such a field is discussed and it is noted that, according to current renormalization theory, for a state ¦M to have finite energy density its associated anticommutator function $\left\langle {M\left\| {\widehat\phi \left( x \right)\widehat\phi \left( {x'} \right) + \widehat\phi \left( {x'} \right)\widehat\phi \left( x \right)} \right\|M} \right\rangle$ must be of a particular form first discussed by Hadamard. This restriction is shown to lead to a constraint on the construction of the Hilbert space of physical states. This constraint is used to reject a recently proposed scheme for the construction of this space which was based on a principle of energy minimization.This essay received an honourable mention from the Gravity Research Foundation for the year 1984.-Ed.

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