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On the graded group U(1/1)

Journal Article · · Journal of Mathematical Physics (New York); (United States)
DOI:https://doi.org/10.1063/1.530406· OSTI ID:6585252
 [1]
  1. 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