On the dimensional reduction procedure

The issue related to the so-called dimensional reduction procedure is revisited within the Euclidean formalism. First, it is shown that for symmetric spaces, the local exact heat-kernel density is equal to the reduced one, once the harmonic sum has been successfully performed. In the general case, due 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 contributions in the short t expansion. Implications of these results with regard to dimensional-reduction anomaly are discussed. (C) 2001 Published by Elsevier Science B.V.