On the dimensional reduction procedure

The issue related to the so-called dimensional reduction procedure is revis ited within the Euclidean formalism. First, it is shown that for symmetric spaces, the local exact heat-kernel density is equal to the reduced one, on ce the harmonic sum has been successfully performed. In the general case, d ue to the impossibility to deal with exact results, the short t heat-kernel asymptotics is considered. It is found that the exact heat-kernel and the dimensionally reduced one coincide up to two nontrivial leading contributio ns in the short t expansion. Implications of these results with regard to d imensional-reduction anomaly are discussed. (C) 2001 Published by Elsevier Science B.V.