Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-11-06
Phys.Rev. D70 (2004) 084047
Physics
High Energy Physics
High Energy Physics - Theory
revtex4, 9 pages
Scientific paper
10.1103/PhysRevD.70.084047
Analytical approximations for $< \phi^2 >$ 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 $\xi$ to the scalar curvature, and in a zero or nonzero temperature vacuum state. The expression for $< \phi^2 >$ 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 $< \phi^2 >$ 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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