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

Romeo Brunetti, Klaus Fredenhagen, Martin Köhler
October 27, 1995
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.
open access link Commun.Math.Phys. 180 (1996) 633-652
@article{Brunetti:1995rf, author = "Brunetti, R. and Fredenhagen, K. and Kohler, M.", title = "{The Microlocal spectrum condition and Wick polynomials of free fields on curved space-times}", journal = "Commun. Math. Phys.", volume = "180", year = "1996", pages = "633-652", doi = "10.1007/BF02099626", eprint = "gr-qc/9510056", archivePrefix = "arXiv", primaryClass = "gr-qc", reportNumber = "DESY-95-196", SLACcitation = "%%CITATION = GR-QC/9510056;%%" }

Keywords: 
QFT on curved spacetimes, microlocal spectrum condition, Hadamard states