Green functions and dimensional reduction of quantum fields on product manifolds

Details Green functions and dimensional reduction of quantum fields on product manifolds Green functions and dimensional reduction of quantum fields on product manifolds

2007-09-20

arxiv.org/abs/0709.3227v2

Class.Quant.Grav.25:075005,2008

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

10.1088/0264-9381/25/7/075005

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.

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