On the graded group U(1/1)
Journal Article
·
· Journal of Mathematical Physics (New York); (United States)
- Lawrence Berkeley Laboratory, Nuclear Science Division, University of California, Berkeley, California 94720 (United States)
A noncanonical parametrization for the graded group U(1/1) is introduced similar to the Euler angles for the ordinary group SU(2). Two differential representations for the underlying algebra of U(1/1) are constructed on the full and the restricted, i.e., coset, parameter space, respectively. A space of functions living on the latter is found exhibiting close formal similarities to a Hilbert space. Remarkably, the indices of those functions and thus the orthogonality and completeness relations involve anticommuting variables. Using this Hilbert space a representation of U(1/1) is evaluated which shows analogies to the Wigner functions for SU(2).
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 6585252
- Journal Information:
- Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 34:6; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
661100* -- Classical & Quantum Mechanics-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
GRADED LIE GROUPS
HILBERT SPACE
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL SPACE
ROTATIONAL INVARIANCE
SPACE
SPHERICAL HARMONICS
SU GROUPS
SU-2 GROUPS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
U GROUPS
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
GRADED LIE GROUPS
HILBERT SPACE
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL SPACE
ROTATIONAL INVARIANCE
SPACE
SPHERICAL HARMONICS
SU GROUPS
SU-2 GROUPS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
U GROUPS