On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces

Details On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces

1995-05-09

arxiv.org/abs/gr-qc/9505009v1

J.Geom.Phys. 20 (1996) 1-18

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

45 pages, latex, no figures

Scientific paper

10.1016/0393-0440(95)00042-9

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.

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