The Microlocal Spectrum Condition and Wick Polynomials of Free Fields on Curved Spacetimes

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” (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. Date: February 7, 2008. e-mail: [email protected]. e-mail: [email protected]. e-mail: [email protected].