The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
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 npoint 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 twopoint 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 energymomentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our “microlocal spectrum condition”.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 October 1996
 DOI:
 10.1007/BF02099626
 arXiv:
 arXiv:grqc/9510056
 Bibcode:
 1996CMaPh.180..633B
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 21 pages, AMSLaTeX, 2 figures appended as Postscript files