An application of the division algebras, Jordan algebras and split composition algebras

Journal Article · Mon Jul 20 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92001964· OSTI ID:6991866

Foot, R; Joshi, G C ^[1]

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1. Melbourne Univ., Parkville (Australia). School of Physics

It has been established that the covering group of the Lorentz group in D = 3, 4, 6, 10 can be expressed in a unified way, based on the four composition division algebras R, C, Q and O. In this paper, the authors discuss, in this framework, the role of the complex numbers of quantum mechanics. A unified treatment of quantum-mechanical spinors is given. The authors provide an explicit demonstration that the vector and spinor transformations recently constructed from a subgroup of the reduced structure group of the Jordan algebras M{sup n}{sub 3} are indeed the Lorentz transformations. The authors also show that if the division algebras in the construction of the covering groups of the Lorentz groups in D = 3, 4, 6, 10 are replaced by the split composition algebras, then the sequence of groups SO(2, 2), SO(3, 3) and SO(5, 5) result. The analysis is presumed to be self-contained as the relevant aspects of the division algebras and Jordan algebras are reviewed. Some applications to physical theory are indicated.

• OSTI ID: 6991866
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:18; ISSN IMPAE; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
DOCUMENT TYPES
LIE GROUPS
LORENTZ GROUPS
MATHEMATICS
MECHANICS
POINCARE GROUPS
QUANTUM MECHANICS
REVIEWS
SPINORS
SYMMETRY GROUPS
TENSORS
TRANSFORMATIONS
USES
VECTORS