On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
General Relativity and Quantum Cosmology
2009-10-28 v1
Abstract
The eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces of arbitrary dimension are computed by separating variables in geodesic polar coordinates. These eigenfunctions are used to derive the heat kernel of the iterated Dirac operator on these spaces. They are then studied as cross sections of homogeneous vector bundles, and a group-theoretic derivation of the spinor spherical functions and heat kernel is given based on Harish-Chandra's formula for the radial part of the Casimir operator.
Keywords
Cite
@article{arxiv.gr-qc/9505009,
title = {On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces},
author = {R. Camporesi and A. Higuchi},
journal= {arXiv preprint arXiv:gr-qc/9505009},
year = {2009}
}
Comments
45 pages, latex, no figures