1303.5253 (R. Kumar et al.)

General N = 2 Supersymmetric Quantum Mechanical Model: Novel Discrete
Symmetries    [PDF]

R. Kumar, R. P. Malik

In addition to the usual supersymmetric (SUSY) continuous symmetry transformations for a general N = 2 SUSY quantum mechanical model, we show the existence of a set of novel discrete symmetry transformations for the Lagrangian of the above SUSY theory. Out of all these discrete symmetry transformations, a unique discrete transformation corresponds to the Hodge duality operation of differential geometry and the above SUSY continuous symmetry transformations correspond to the de Rham cohomological operators of differential geometry. Thus, we provide a concrete proof of our earlier conjecture that any arbitrary N = 2 SUSY quantum mechanical model is an example of a Hodge theory where the cohomological operators find their physical realizations in the language of symmetry transformations. Possible physical implications are mentioned, too.

View original: http://arxiv.org/abs/1303.5253