  We introduce a new localization principle which is a generalized canonical
transformation. It unifies BRST localization, the non-abelian localization
principle and a special case of the conformal Duistermaat-Heckman integration
formula of Paniak, Semenoff and Szabo. The heat kernel on compact Lie groups is
localized in two ways. First using a non-abelian generalization of the
derivative expansion localization of Palo and Niemi and secondly using the BRST
localization principle and a configuration space path integral. In addition we
present some new formulas on homogeneous spaces which might be useful in a
possible localization of Selberg's trace formula on locally homogeneous spaces.
