On generalized Clifford algebras and their physical applications
May, 2010Citations per year
Abstract: (arXiv)
Generalized Clifford algebras (GCAs) and their physical applications were extensively studied for about a decade from 1967 by Alladi Ramakrishnan and his collaborators under the name of L-matrix theory. Some aspects of GCAs and their physical applications are outlined here. The topics dealt with include: GCAs and projective representations of finite abelian groups, Alladi Ramakrishnan's sigma operation approach to the representation theory of Clifford algebra and GCAs, Dirac's positive energy relativistic wave equation, Weyl-Schwinger unitary basis for matrix algebra and Alladi Ramakrishnan's matrix decomposition theorem, finite-dimensional Wigner function, finite-dimensional canonical transformations, magnetic Bloch functions, finite-dimensional quantum mechanics, and the relation between GCAs and quantum groups.Note:
- Dedicated to the memory of Professor Alladi Ramakrishnan
- Clifford algebra
- generalized Clifford algebras
- projective representations of finite abelian groups
- L-matrix theory
- Dirac equation
- Dirac's positive-energy relativistic wave equation
- dark matter
- Heisenberg-Weyl commutation relation
- finite-dimensional Wigner function
- finite-dimensional canonical transformations
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