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Analytical approximation for $< ϕ^2 >$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes

Arkady A. Popov
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Abstract

Analytical approximations for $< ϕ^2 >$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $ξ$ to the scalar curvature, and in a zero or nonzero temperature vacuum state. The expression for $< ϕ^2 >$ is divided into low- and high-frequency parts. The expansion for the high-frequency contribution to this quantity is obtained. This expansion is analogous to the DeWitt-Schwinger one. As an example, the low-frequency contribution to $< ϕ^2 >$ is calculated on the background of the small perturbed flat spacetime in a quantum state corresponding to the Minkowski vacuum at the asymptotic. The limits of the applicability of these approximations are discussed.

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Arkady A. Popov. 2004-11-06. Analytical approximation for $< ϕ^2 >$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes. https://doi.org/10.1103/physrevd.70.084047

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