Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-03-27
Nucl.Phys. B511 (1998) 737-759
Physics
High Energy Physics
High Energy Physics - Theory
27 pages, 1 figure, uses harvmac, epsf and boldmath (included). Change of title and some text changes, form to be published
Scientific paper
10.1016/S0550-3213(97)00667-6
The weak energy condition is known to fail in general when applied to expectation values of the the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states $|\psi \r$ for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural restriction on $|\psi \r$ is suggested and illustrated by two quantum mechanical examples based on a simple perturbed harmonic oscillator Hamiltonian. The proposed alternative quantum weak energy condition is applied to states formed by the action of scalar, vector and the energy momentum tensor operators on the vacuum. We assume conformal invariance in order to determine almost uniquely three-point functions involving the energy momentum tensor in terms of a few parameters. The positivity conditions lead to non trivial inequalities for these parameters. They are satisfied in free field theories, except in one case for dimensions close to two. Further restrictions on $|\psi \r$ are suggested which remove this problem. The inequalities which follow from considering the state formed by applying the energy momentum tensor to the vacuum are shown to imply that the coefficient of the topological term in the expectation value of the trace of the energy momentum tensor in an arbitrary curved space background is positive, in accord with calculations in free field theories.
Latorre Jose Ignacio
Osborn Herbert
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