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On the supersymmetry group of the classical Bose-Fermi oscillator. (English) Zbl 1136.81378

Summary: Applying the concept of a momentum map for supersymplectic supervectorspaces to the one-dimensional Bose-Fermi oscillator, we show that the largest symmetry group that admits a momentum map is the identity component of the intersection of the orthosymplectic group \(\text{OSp}(2|2)\) and the group of supersymplectic transformations. This gives a systematic characterization of a certain class of odd supersymmetry transformations that were originally introduced in an ad hoc way.

MSC:

81Q60 Supersymmetry and quantum mechanics
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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