  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.
