Abstract
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).
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