On the stress-energy tensor of quantum fields in curved spacetimes-comparison of different regularization schemes and symmetry of the Hadamard/Seeley-DeWitt coefficients

We review a few rigorous and partly unpublished results on the regularization of the stress-energy in quantum field theory on curved spacetimes: (1) the symmetry of the Hadamard Seeley-DeWitt coefficients in smooth Riemannian and Lorentzian spacetimes, (2) the equivalence of the local ζ-function and...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-09, Vol.45 (37), p.374019
Main Authors: Hack, Thomas-Paul, Moretti, Valter
Format: Article
Language:English
Subjects:
Hadamard coefficients
Hadamard states
heat kernel
QFT in curved spacetime
Seeley-DeWitt coefficients
stress-energy tensor
zeta function
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Summary:We review a few rigorous and partly unpublished results on the regularization of the stress-energy in quantum field theory on curved spacetimes: (1) the symmetry of the Hadamard Seeley-DeWitt coefficients in smooth Riemannian and Lorentzian spacetimes, (2) the equivalence of the local ζ-function and the Hadamard-point-splitting procedure in smooth static spacetimes and (3) the equivalence of the DeWitt-Schwinger- and the Hadamard-point-splitting procedure in smooth Riemannian and Lorentzian spacetimes. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to 'Applications of zeta functions and other spectral functions in mathematics and physics'.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/37/374019