PROBABILITY DISTRIBUTION FUNCTIONAL FOR EQUAL-TIME CORRELATION FUNCTIONS IN CURVED SPACE

20 January 1994

journal article
Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics A

Vol. 9 (2) , 221-238
https://doi.org/10.1142/s0217751x9400011x

Abstract

We present a systematic method to calculate the probability distribution functional (PDF) for spatial configuration of an interacting field in curved space-time. As an example, we consider PDF for the minimally coupled massive λΦ⁴ theory up to the first order of the coupling constant and evaluate it both in Minkowski and de Sitter spacetimes. We observe that PDF has an ultraviolet divergence even after the ultraviolet renormalization. This divergence is unavoidable to reproduce finite expectation values; thus some kind of regularization is necessary to write down PDF. As an application of it, a scaling law among multipoint correlation functions in the de Sitter space is found.

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