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Generalized Gelfand-Naimark-Segal construction for supersymmetric quantum mechanics

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Abstract

The consistent treatment of anticommuting parameters in quantum theories requires the introduction of the Hilbert Q module with a Q scalar product (where Q is infinite-dimensional Grassman-Banach algebra). The extended GNS construction for representations of Q algebras on such Q modules is given.

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References

  1. Casalbuoni, R., Nuovo Cim. 33A, 115 (1976).

    Google Scholar 

  2. De Witt, B., Supermanifolds, Cambridge Univ. Press, Cambridge, 1984.

    Google Scholar 

  3. Frydryszak, A., Nonrelativistic Pseudomechanics, Wrocław Univ. thesis 1981, unpublished (in Polish).

  4. Bongaarts, P. Anticommuting c-numbers in quantum theory, Leiden Univ. preprint, September 1983.

  5. Grosse, H. and Pittner, L., J. Phys A: Math. Gen. 20, 4265 (1987).

    Article  Google Scholar 

  6. Witten, E., Nucl. Phys. B195, 513 (1981).

    Article  Google Scholar 

  7. Salomonson, P. and Van Holten, J. W., Nucl. Phys. B196, 509 (1982).

    Article  Google Scholar 

  8. Cooper, F. and Freedman, B., Ann. Phys. 146, 262 (1983).

    Article  Google Scholar 

  9. Takeda, G. and Ui, H., Progr. Theor. Phys. 73, 1061 (1985).

    Google Scholar 

  10. De Azcárraga, J. A., Lukierski, J., and Vindel, P., Mol. Phys. Lett. A1, 293 (1986).

    Google Scholar 

  11. Rogers, A., J. Math. Phys. 21, 1352 (1981).

    Article  Google Scholar 

  12. Jadczyk, A. Z. and Pilch, K., Commun. Math. Phys. 78, 373 (1981).

    Google Scholar 

  13. Frydryszak, A. and Jakóbczyk, L. Algebraic aspects of supersymmetric quantum mechanics with anticommuting co-ordinates, Wrocław Univ. preprint.

  14. Bratelli, O. and Robinson, D. W., Operator Algebras and Quantum Statistical Mechanics, Vol. 2, Springer-Verlag, New York, 1981.

    Google Scholar 

  15. Glauber, R. J., Phys. Rev. 130, 2539 (1963).

    Article  Google Scholar 

  16. Jakóbczyk, L., Ann. Phys. 161, 314 (1985).

    Article  Google Scholar 

Download references

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Author notes

  1. A. Frydryszak

    Present address: Institute of Theoretical Physics, University of Wrocław, Wrocław, Poland

Authors and Affiliations

  1. Department of Physics, University of Firenze, Firenze, Italy

    A. Frydryszak

  2. Institute of Theoretical Physics, University of Wrocław, Wrocław, Poland

    L. Jakóbczyk

Authors
  1. A. Frydryszak
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  2. L. Jakóbczyk
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Frydryszak, A., Jakóbczyk, L. Generalized Gelfand-Naimark-Segal construction for supersymmetric quantum mechanics. Letters in Mathematical Physics 16, 101–107 (1988). https://doi.org/10.1007/BF00402016

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  • DOI: https://doi.org/10.1007/BF00402016

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