Heat Kernel Asymptotics on Homogeneous Bundles
Differential Geometry
2015-05-13 v1 High Energy Physics - Theory
Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal solution correctly reproduces the exact heat kernel diagonal after a suitable regularization and analytical continuation.
Cite
@article{arxiv.0708.0234,
title = {Heat Kernel Asymptotics on Homogeneous Bundles},
author = {Ivan G. Avramidi},
journal= {arXiv preprint arXiv:0708.0234},
year = {2015}
}
Comments
29 pages, Proceedings of the 2007 Midwest Geometry Conference in Honor of Thomas P. Branson