Green functions and dimensional reduction of quantum fields on product manifolds

Abstract

We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this approximation. We show that for large distances on N the remainder is small. If P=R^{D-1}xS^{beta}, where S^{beta} is a circle of radius beta, then the result reduces to the well-known approximation of the D dimensional finite temperature quantum field theory to D-1 dimensional one in the high temperature limit. Analytic continuation of Euclidean fields is discussed briefly.

17 pages

References in corpus (2)

• Quantum Field Theory on Curved Backgrounds, I. The Euclidean Functional Integral
• Green functions and Euclidean fields near the bifurcate Killing horizon

Cited by in corpus (2)

• Universal properties of the near-horizon optical geometry
• Euclidean scalar Green functions near the black hole and black brane horizons