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

  • R. KumarEmail author
  • R. P. Malik
Regular Article - Theoretical Physics


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.


Discrete Symmetry Symmetry Transformation Exterior Derivative Duality Transformation Hodge Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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


  1. 1.
    E. Witten, Nucl. Phys. B 188, 513 (1981) ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 264 (1995) MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    A. Das, Field Theory: A Path Integral Approach (World Scientific, Singapore, 1993) Google Scholar
  4. 4.
    R. Kumar, R.P. Malik, Europhys. Lett. 98, 11002 (2012) ADSCrossRefGoogle Scholar
  5. 5.
    R.P. Malik, A. Khare, Ann. Phys. 334, 142 (2013) ADSCrossRefGoogle Scholar
  6. 6.
    R.P. Malik, Int. J. Mod. Phys. A 22, 3521 (2007) MathSciNetADSCrossRefzbMATHGoogle Scholar
  7. 7.
    R.P. Malik, Mod. Phys. Lett. A 15, 2079 (2000) MathSciNetADSCrossRefzbMATHGoogle Scholar
  8. 8.
    R.P. Malik, Mod. Phys. Lett. A 16, 477 (2001) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    S. Gupta, R.P. Malik, Eur. Phys. J. C 58, 517 (2008) MathSciNetADSCrossRefzbMATHGoogle Scholar
  10. 10.
    R. Kumar, S. Krishna, A. Shukla, R.P. Malik, Eur. Phys. J. C 72, 2188 (2012) ADSCrossRefGoogle Scholar
  11. 11.
    R. Kumar, S. Krishna, A. Shukla, R.P. Malik. arXiv:1203.5519 [hep-th]
  12. 12.
    R.P. Malik, J. Phys. A, Math. Gen. 41, 4167 (2001) MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    E. Witten, Commun. Math. Phys. 17, 353 (1988) MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    A.S. Schwarz, Lett. Math. Phys. 2, 247 (1978) ADSCrossRefzbMATHGoogle Scholar
  15. 15.
    F. Cooper, B. Freedman, Ann. Phys. 146, 262 (1983) MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    A. Lahiri, P.K. Roy, B. Bagchi, Int. J. Mod. Phys. A 5, 1383 (1990) MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    T. Eguchi, P.B. Gilkey, A. Hanson, Phys. Rep. 66, 213 (1980) MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    S. Mukhi, N. Mukunda, Introduction to Topology, Differential Geometry and Group Theory for Physicists (Wiley, New Delhi, 1990) zbMATHGoogle Scholar
  19. 19.
    K. Nishijima, Prog. Theor. Phys. 80, 897 (1988) MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    S. Deser, A. Gomberoff, M. Henneaux, C. Teitelboim, Phys. Lett. B 400, 80 (1997) MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    S. Gupta, R. Kumar, R.P. Malik. arXiv:0908.2561 [hep-th]
  22. 22.
    F. Correa, V. Jakubsky, L. Nieto, M.S. Plyushchay, Phys. Rev. Lett. 101, 030403 (2008) MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    F. Correa, V. Jakubsky, M.S. Plyushchay, J. Phys. A 41, 485303 (2008) MathSciNetCrossRefGoogle Scholar
  24. 24.
    M. de Crombrugghe, V. Rittenberg, Ann. Phys. 151, 99 (1983) ADSCrossRefGoogle Scholar
  25. 25.
    A. Khare, J. Maharana, Nucl. Phys. B 244, 409 (1984) MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    R.P. Malik et al. (in preparation) Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Department of Physics, Center of Advanced Studies, Faculty of ScienceBanaras Hindu UniversityVaranasiIndia
  2. 2.DST Center for Interdisciplinary Mathematical Sciences, Faculty of ScienceBanaras Hindu UniversityVaranasiIndia

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