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

Journal of Geometry and Physics

Volumn 20, Issue 1, 1996, Pages 1-18

  Camporesi, Roberto ^a   Higuchi, Atsushi ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF BERN   (Switzerland)

Author keywords

Dirac operator; Eigenfunctions

Indexed keywords

EID: 0030242191     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/0393-0440(95)00042-9     Document Type: Article

References (16)

1. A.O. Barut and R. Raczka, Theory of Group Representations and Applications (World Scientific, Singapore, 1986).
2. R. Camporesi, Harmonic analysis and propagators on homogeneous spaces, Phys. Rep. 196 (1990) 1.
3. R. Camporesi, The spinor heat kernel in maximally symmetric spaces, Comm. Math. Phys. 148 (1992) 283-308.
4. R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217-4246.
5. R. Camporesi and A. Higuchi, The Plancherel measure for p-forms in real hyperbolic spaces, J. Geom. Phys. 15 (1994) 57-94.
6. R. Camporesi, The spherical transform for homogeneous vector bundles over hyperbolic spaces, preprint (1993).
7. Y. Choquet-Bruhat, C. DeWitt-Morette and M. Dillard-Bleick, Analysis, Manifolds and Physics, Revised Ed. (North-Holland, Amsterdam, 1982).
8. L. Dabrowski and A. Trautman, Spinor structures on spheres and projective spaces, J. Math. Phys. 27 (1986) 2022-2028.
9. I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products, Revised Ed. (Academic Press, New York, 1980).
10. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces (Academic Press, New York, 1978).
11. A. Knapp, Representation Theory of Semisimple Groups, an Overview based on Examples (Princeton University Press, Princeton, NJ, 1986).
12. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vols. I and II (Interscience, New York, 1969).
13. J. Milnor, Spin structures on manifolds, L'Enseignement Math. 9 (1963) 198-203.
14. E. Thieleker, On the integrable and square-integrable representations of Spin(1,2m), Trans. Amer. Math. Soc. 230 (1977) 1-40.
15. A. Trautman, Spin structures on hypersurfaces and the spectrum of the Dirac operator on spheres, in: Spinors, Twistors, Clifford Algebras and Quantum Deformations (Kluwer Academic Publishers, Dordrecht, 1993).
16. N.R. Wallach, Harmonic Analysis on Homogeneous Spaces (Marcel Dekker, New York, 1973).