Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-09-13
Commun.Math.Phys. 232 (2003) 189-221
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
35 pages, no figure, LaTeX2e. Final form accepted for publication in Commun.Math.Phys
Scientific paper
10.1007/s00220-002-0702-7
Hollands and Wald's technique based on *-algebras of Wick products of field operators is strightforwardly generalized 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. The proposed stress-energy tensor operator is 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. They are independent from the arbitrary length scale (and any quantum state) and they classically vanish on solutions of field equation. The averaged stress-energy tensor with respect to Hadamard quantum states can be obtained by an improved point-splitting renormalization procedure which makes use of the nonambiguous part of the Hadamard parametrix only that is completely determined by the local geometry and the parameters which appear in the Klein-Gordon operator. The averaged stress-energy tensor also coincides with that found by employing the local $\zeta$-function approach.
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