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arxiv 1303.5253 v3 pith:7AOBWSUO submitted 2013-03-21 hep-th

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

classification hep-th
keywords susysymmetrytransformationsdiscretemechanicalmodelquantumphysical
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In addition to the usual supersymmetric (SUSY) continuous symmetry transformations for the 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 quantum mechanical model. 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 (and their anticommutator) provide the physical realizations of 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 of this theory. Possible physical implications of our present study are pointed out, too.

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