Comments on the Stress-Energy Tensor Operator in Curved Spacetime
By Valter Moretti. 2001
154 citations recorded by the source corpus.
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 gαβQ and no arbitrary smooth part of the Hadamard parametrix (generated by some arbitrary smooth term ``ω0'') 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.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/66cdcbf11bbce22156e1a45f4408b7ebf03770cf
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Citations in the corpus
- Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime (2001, background): “We are currently investigating this issue; see also [16].”
- Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction (2014, background): “Moreover, without this additional term, the above definition of :Tab:H would not yield a conserved stresstensor expectation value (see [48] Theorem 2.”
- Conservation of the Stress Tensor in Perturbative Interacting Quantum Field Theory in Curved Spacetimes (2004, methodology): “By contrast, Moretti [17] allows modifications to the formula for the stress-energy tensor that are proportional to φPφ and thus vanish classically.”