Singularity structure of the two-point function in quantum field theory in curved spacetime, II
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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|φ(x) φ(y) + φ(y) φ(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.
author list (cited authors)
Fulling, S. A., Narcowich, F. J., & Wald, R. M.