Comments on the Stress-Energy Tensor Operator in Curved Spacetime |
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Authors: | Valter Moretti |
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Institution: | (1) Department of Mathematices, Trento University, 38050 Povo (TN), Italy. E-mail: moretti@science.unitn.it, IT |
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Abstract: | The technique based on a *-algebra of Wick products of field operators in curved spacetime, in the local covariant version
proposed by Hollands and Wald, is strightforwardly generalized in order to define the stress-energy tensor operator in curved
globally hyperbolic spacetimes. In particular, the locality and covariance requirement is generalized to Wick products of
differentiated quantum fields. Within the proposed formalism, there is room to accomplish all of the physical requirements
provided that known problems concerning the conservation of the stress-energy tensor are assumed to be related to the interface
between the quantum and classical formalism. The proposed stress-energy tensor operator turns out to be conserved and reduces
to the classical form if field operators are replaced by classical fields satisfying the equation of motion. The definition
is based on the existence of convenient counterterms given by certain local Wick products of differentiated fields. These
terms are independent from the arbitrary length scale (and any quantum state) and they classically vanish on solutions of
the Klein-Gordon equation. Considering the averaged stress-energy tensor with respect to Hadamard quantum states, the presented
definition turns out to be equivalent to an improved point-splitting renormalization procedure which makes use of the nonambiguous
part of the Hadamard parametrix only that is determined by the local geometry and the parameters which appear in the Klein-Gordon
operator. In particular, no extra added-by-hand term g
αβQ
and no arbitrary smooth part of the Hadamard parametrix (generated by some arbitrary smooth term ``ω
0
') are involved. The averaged stress-energy tensor obtained by the point-splitting procedure also coincides with that found
by employing the local ζ-function approach whenever that technique can be implemented.
Received: 24 September 2001/Accepted: 14 May 2002 Published online: 22 November 2002 |
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