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In addition to the usual supersymmetric (SUSY) continuous symmetrytransformations for the general N = 2 SUSY quantum mechanical model, we showthe existence of a set of novel discrete symmetry transformations for theLagrangian of the above SUSY quantum mechanical model. Out of all thesediscrete symmetry transformations, a unique discrete transformation correspondsto the Hodge duality operation of differential geometry and the above SUSYcontinuous symmetry transformations (and their anticommutator) provide thephysical realizations of the de Rham cohomological operators of differentialgeometry. Thus, we provide a concrete proof of our earlier conjecture that anyarbitrary N= 2 SUSY quantum mechanical model is an example of a Hodge theorywhere the cohomological operators find their physical realizations in thelanguage of symmetry transformations of this theory. Possible physicalimplications of our present study are pointed out, too.

Novel discrete symmetries in the general N = 2 supersymmetric quantum mechanical model