On Generalized Clifford Algebras and their Physical Applications

Ramaswamy Jagannathan ()
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Ramaswamy Jagannathan: Chennai Mathematical Institute

A chapter in The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, 2010, pp 465-489 from Springer

Abstract: Summary 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 σ-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.

Keywords: 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; Finite-dimensional quantum mechanics; Kinematic confinement of quarks; Magnetic Bloch functions; Quantum groups (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6263-8_28

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DOI: 10.1007/978-1-4419-6263-8_28

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