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The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
Open accessAbstract
Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the correspondingn-point distributions, called “microlocal spectrum condition” (μSC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our “microlocal spectrum condition”.
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The Analysis of Linear Partial Differential Operators I
Hörmander, L. (1998) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-642-96750-4 · Cited by 5,721
Haag, R. (1996) · doi:10.1007/978-3-642-61458-3 · Cited by 2,443
Hörmander, L. (1971) · Acta Mathematica · doi:10.1007/bf02392052 · Cited by 2,306
(1994) · Cited by 1,630
The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis
Hörmander, L. (2003) · Classics in Mathematics · doi:10.1007/978-3-642-61497-2 · Cited by 1,345
An algebraic approach to quantum field theory
Haag, R., & Kastler, D. (1964) · Journal of Mathematical Physics · doi:10.1063/1.1704187 · Cited by 1,250
Aspects of Quantum Field Theory in Curved Space-Time
Fulling, S. A. (1989) · doi:10.1017/cbo9781139172073 · Cited by 1,121
Radiation damping in a gravitational field
DeWitt, B. S., & Brehme, R. W. (1960) · Annals of Physics · doi:10.1016/0003-4916(60)90030-0 · Cited by 789
Kay, B. S., & Wald, R. M. (1991) · Physics Reports · doi:10.1016/0370-1573(91)90015-e · Cited by 574
Fourier integral operators. II
Duistermaat, J. J., & Hörmander, L. (1972) · Acta Mathematica · doi:10.1007/bf02392165 · Cited by 574
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Fewster, C. J. (1999) · arXiv · doi:10.48550/arxiv.gr-qc/9910060 · Cited by 134
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Metadata
- Authors
- Brunetti, R., Fredenhagen, K., & Köhler, M.
- Venue
- Communications in Mathematical Physics
- Published
- 1996-10
- Volume
- 180
- Issue
- 3
- Pages
- 633-652
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2003470918
- Cited by
- 258
- References
- 25
- FWCI
- 11.97
- Type
- journal article
- Language
- en
- Open access
- green
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