On generalized Clifford algebras and their physical applications

Details On generalized Clifford algebras and their physical applications On generalized Clifford algebras and their physical applications

2010-05-24

arxiv.org/abs/1005.4300v1

Physics

Mathematical Physics

30 pages; Dedicated to the memory of Prof. Alladi Ramakrishnan; To appear in "The Legacy of Alladi Ramakrishnan in the Mathema

Scientific paper

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.

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