Real representations of finite Clifford algebras. I. Classification
Journal Article
·
· Journal of Mathematical Physics (New York); (USA)
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (USA)
A classification of real matrix irreducible representations of finite-dimensional real Clifford algebras has been made. In contrast to the case of complex representation, three distinct types of representations can be obtained which we call normal, almost complex, and quaternionic. The dimension of the latter two cases is twice as large as that of the normal representation. A criteria for a given Clifford algebra to possess a particular type of the representations is also given with some applications.
- DOE Contract Number:
- AC02-76ER13065
- OSTI ID:
- 5535688
- Journal Information:
- Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 32:7; ISSN 0022-2488; ISSN JMAPA
- Country of Publication:
- United States
- Language:
- English
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657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLASSIFICATION
CLIFFORD ALGEBRA
COMMUTATION RELATIONS
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657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLASSIFICATION
CLIFFORD ALGEBRA
COMMUTATION RELATIONS
DIRAC OPERATORS
IRREDUCIBLE REPRESENTATIONS
MATHEMATICAL OPERATORS
MATRICES
QUANTUM OPERATORS