On the Supersymmetry Group of the Classical Bose-Fermi Oscillator,"

We define the concept of a momentum map for supersymplectic supervectorspaces, and prove the super version of a well-known variation of Noether’s theorem from classical symplectic mechanics. We then characterize the largest supermatrix group that admits a momentum map for the one dimensional supersymmetric harmonic oscillator. It is the identity component of the intersection of the orthosymplectic group OSp(2|2) and the stabilizer of the supersymplectic form. It is also obtained from exponentiating a certain well-known clas of infinitesimal supersymmetries. Our treatment is mathematically rigorous. It is based on the concept of an A-manifold developed by G. M. Tuynman.