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Contributions of Alladi Ramakrishnan to the Mathematical Sciences Read chapter Read first chapter

2010 | OriginalPaper | Chapter

On Generalized Clifford Algebras and their Physical Applications

Author : Ramaswamy Jagannathan

Published in: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Publisher: Springer New York

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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.

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previous chapter A Statistical Model for the Quark Structure of the Nucleon
next chapter (p, q)-Rogers-Szegö Polynomial and the (p, q)-Oscillator
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Metadata
Title
On Generalized Clifford Algebras and their Physical Applications
Author
Ramaswamy Jagannathan
Copyright Year
2010
Publisher
Springer New York
Book
The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Print ISBN: 978-1-4419-6262-1

Electronic ISBN: 978-1-4419-6263-8

Copyright Year: 2010

DOI
https://doi.org/10.1007/978-1-4419-6263-8_28

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