On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces |
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| Institution: | 1. Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy;2. Institut für theoretische Physik, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland;1. Department of Mathematics, University of Aizu, 965-8580, Aizuwakamatsu, Japan;2. Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA;1. Department of Physics, University of Tehran, P.O. Box 14395-547, Tehran, Iran;2. School of Physics, Institute for Research in Fundamental Sciences, (IPM), Tehran 19395-5531, Iran;1. Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CC 51-Place Eugène Bataillon, 34095 Montpellier cedex 5, France;2. Institut Camille Jordan, Université Lyon 1, 69622 Villeurbanne cedex, France;1. Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;2. Department of Physics and Astronomy, and Stewart Blusson Quantum Matter Institute, The University of British Columbia, Vancouver, B.C. V6T 1Z1, Canada;1. Department of Physics, Princeton University, United States of America;2. Department of Applied Physics and Applied Mathematics and Department of Mathematics, Columbia University, United States of America |
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| 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. |
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