THE HEAT KERNEL IN CURVED SPACE IN TERMS OF CLASSICAL VARIABLES

Abstract

Using functional methods introduced by Onofri, the heat kernel matrix element Mxy=<x|e-Ht|y> for an elliptic operator H in curved space is unambiguously represented in terms of functional derivatives of an expression which solely involves classical variables. To illustrate how this can be used, the lowest order term in the Schwinger–DeWitt expansion for Mxx is computed.