The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

Details The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

1995-10-27

arxiv.org/abs/gr-qc/9510056v1

Commun.Math.Phys. 180 (1996) 633-652

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, AMS-LaTeX, 2 figures appended as Postscript files

Scientific paper

10.1007/BF02099626

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 corresponding n-point distributions, called ``microlocal spectrum condition'' ($\mu$SC). 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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