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 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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Brunetti, R., Fredenhagen, K. & Köhler, M. The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes. Commun.Math. Phys. 180, 633–652 (1996). https://doi.org/10.1007/BF02099626
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DOI: https://doi.org/10.1007/BF02099626