SINGULARITY STRUCTURE OF THE 2-POINT FUNCTION IN QUANTUM-FIELD THEORY IN CURVED SPACETIME .2.
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We prove that, for a massive, scalar, quantum field in a wide class of static spacetimes, the two-point function 0|(x) (y) + (y) (x)|0 has singularity structure of the Hadamard form. In particular, this implies that the point-splitting renormalization prescription is well defined in these spacetimes. As a corollary of this result and a previous result of Fulling. Sweeny, and Wald, we show that in an arbitrary globally hyperbolic spacetime there always exists a large class of states for which the singular part of the two-point function has the Hadamard form. In addition, we prove that, for a closed universe which is both initially and finally static, the S-matrix exists. 1981.