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

Roberto Camporesi; Atsushi Higuchi

doi:10.1016/0393-0440(95)00042-9

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

Roberto Camporesi^*, Atsushi Higuchi

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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 then 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.

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Journal of Geometry and Physics
Volume	20
Issue number	1
DOIs	https://doi.org/10.1016/0393-0440(95)00042-9
Publication status	Published - 1996

Keywords

Dirac operator
Eigenfunctions

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10.1016/0393-0440(95)00042-9

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AB - 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 then 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.

KW - Dirac operator

KW - Eigenfunctions

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

Abstract

Keywords

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