# Novel discrete symmetries in the general Open image in new window supersymmetric quantum mechanical model

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## Abstract

In addition to the usual supersymmetric (SUSY) continuous symmetry transformations for the general Open image in new window 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 Open image in new window 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.

## Keywords

Discrete Symmetry Symmetry Transformation Exterior Derivative Duality Transformation Hodge Theory## Notes

### Acknowledgements

R.K. would like to express his deep gratitude to the UGC, Government of India, for the financial support through the SRF scheme.

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