Abstract
An operation is described which generates Dirac matrices from Pauli matrices. Repeating this operation leads to matrix representations of higher dimensional Clifford algebras. It is also used to construct matrices satisfying w-commutation relations where w is a root of unity. Further generalisations and the use of these results in forming Lie algebras of physical interest is discussed.
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References
L-Matrix Theory or the Grammar of Dirac Matrices (Tata-McGraw Hill, New Delhi, India, 1972), (This contains the list of papers published in the Journal of Mathematical Analysis and Applications, 1967–72.)
Tories in Numerical Analysis, Ed. J.H. Miller, Academic Press, 132 (1976). (Proceedings of the conference on numerical analysis held in Dublin, Ireland, 1974.)
Symmetries in Science, Ed. Bruno Gruber and R.S. Millman, Plenum Press, New York and London, 323 (1979). (Proceedings of the Einstein Centennial Celebration Science Symposium at Southern Illinois University, Carbondale, Illinois, U.S.A., 1979.)
A. Ramakrishnan, ‘The Dirac Hamiltonian as a member of a hierarchy of matrices’, J. Math. Anal. and Applications, 20, 9–l6, 1967.
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© 1986 D. Reidel Publishing Company
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Ramakrishnan, A. (1986). Clifford Algebra, Its Generalisations and Physical Applications. In: Chisholm, J.S.R., Common, A.K. (eds) Clifford Algebras and Their Applications in Mathematical Physics. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4728-3_48
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DOI: https://doi.org/10.1007/978-94-009-4728-3_48
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8602-8
Online ISBN: 978-94-009-4728-3
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