On Generalized Clifford Algebras and their Physical Applications

Chapter

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.

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 

Notes

Acknowledgement

I dedicate this article, with gratitude, to the memory of my teacher Professor Alladi Ramakrishnan under whose guidance I started my scientific career at MATSCIENCE, The Institute of Mathematical Sciences, Chennai.

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Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Chennai Mathematical InstituteChennaiIndia
  2. 2.The Institute of Mathematical SciencesChennaiIndia

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