Volume 109, Number 3, February 2015
|Number of page(s)||6|
|Section||The Physics of Elementary Particles and Fields|
|Published online||19 February 2015|
A free supersymmetric system: Novel symmetries
1 Physics Department, Centre of Advanced Studies, Banaras Hindu University - Varanasi, 221 005, (U.P.), India
2 DST Centre for Interdisciplinary Mathematical Sciences, Faculty of Science, Banaras Hindu University Varanasi, 221 005, (U.P.), India
3 AS-ICTP - Strada Costiera-11, I-34014, Trieste, Italy
Received: 7 December 2014
Accepted: 21 January 2015
We discuss a set of novel discrete symmetries of a free supersymmetric (SUSY) quantum-mechanical system which is the limiting case of a widely studied interacting SUSY model of a charged particle constrained to move on a sphere in the background of a Dirac magnetic monopole. The usual continuous symmetries of this model provide the physical realization of the de Rham cohomological operators of differential geometry. The interplay between the novel discrete symmetries and usual continuous symmetries leads to the physical realization of the relationship between the (co-)exterior derivatives of differential geometry. We have also exploited the supervariable approach to derive the nilpotent SUSY symmetries of the theory and provided the geometrical origin and interpretation for the nilpotency property. Ultimately, our present study (based on innate symmetries) proves that our free SUSY example is a tractable model for the Hodge theory.
PACS: 11.30.Pb – Supersymmetry / 03.65.-w – Quantum mechanics / 02.40.-k – Geometry, differential geometry, and topology
© EPLA, 2015
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