Abstract
We give a construction of symplectic Clifford algebras according to an algebraic process analogous to the one used in orthogonal Clifford algebras. We define Clifford and spinors groups and symplectic spinors. We develop two applications: first a geometric approach to the Fourier transform, second a deformation theory for the algebras associated with a symplectic manifold.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bourbaki: Groupes et algèbres de Lie. Chapitres 2 et 3. Hermann Paris, 1972
A. Crumeyrolle: a)‘Algèbre de Clifford symplectique.’.etc… J. Math.pures et appl, 56, 1977, p.205-230. b)‘Classes de Maslov, fibrations spinorielles symplectiques et transformation de Fourier’. Ibid, 58, 1979, p.111-120. c)‘Deformations d’algèbres associées à une variété symplectique’… Ann. Inst. Henri Poincaré, vol 35, nΰ3, 1981, p.175-194. d)‘Planck’s constant and symplectic geometry.’ Colloquium on differential geometry, Debrecen 1984. e)’structures symplectiques, structures complexes, spineurs symplectiques et transformation de Fourier.’ Preprint. Toulouse 1985.
R. Howe: ‘On the role of the Heisenberg group in harmonic analysis’! Bull. of the Am. Math. Soc. vol. 3, n°2, Sept.1
M. DeWilde et P. Lecomte: ‘Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds’. Letters in Math. Physics. 7, 1983, 487–496.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 D. Reidel Publishing Company
About this chapter
Cite this chapter
Crumeyrolle, A. (1986). Symplectic Clifford Algebras. In: Chisholm, J.S.R., Common, A.K. (eds) Clifford Algebras and Their Applications in Mathematical Physics. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4728-3_44
Download citation
DOI: https://doi.org/10.1007/978-94-009-4728-3_44
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8602-8
Online ISBN: 978-94-009-4728-3
eBook Packages: Springer Book Archive