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

R. Brunetti·K. Fredenhagen·M. Koehler
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Abstract

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'' ($μ$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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R. Brunetti, K. Fredenhagen, M. Koehler. 1995-10-27. The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes. https://doi.org/10.1007/bf02099626

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