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Quadratic Tomography Star Product Algebra and its Classical Limit

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Abstract

We consider quadratic tomography in star product formalism. The contraction and the behavior of the associative algebra of quadratic tomographic symbols in \(\hbar \rightarrow 0\) limit are discussed. A simple k-deformation example is illustrated.

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References

  1. Wigner, E.P.: Phys. Rev. 40, 749 (1932)

    Article  ADS  Google Scholar 

  2. Weyl, H.: Z. Phys 46, 1–33 (1927)

    Article  ADS  Google Scholar 

  3. Weyl, H.: The theory of groups and quantum mechanics, Dover (1931)

  4. Groenewold, H.J.: Physica 12, 405–460 (1946)

    Article  ADS  MathSciNet  Google Scholar 

  5. Moyal, J.E.: Proc. Cambridge Phil. Soc. 45, 99–124 (1949)

    Article  ADS  Google Scholar 

  6. Curtright, T.L., Fairlie, D.B., Zachos, C.K.: A Concise treatise on Quantum Mechanics in Phase Space World Scientific Publishing (2014)

  7. Glauber, R.J.: Phys. Rev. Lett. 10, 84 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  8. Sudarshan, E.C.G.: Phys. Rev. Lett. 10, 177 (1963)

    Article  ADS  Google Scholar 

  9. Husimi, K.: Proc. Phys. Math. Soc. Jpn 23, 264 (1940)

    Google Scholar 

  10. Cahill, K.E., Glauber, R.J.: Phys. Rev. 177, 1882 (1969)

    Article  ADS  Google Scholar 

  11. Vogel, K., Risken, H.: Phys. Rev. A 40, 2847 (1989)

    Article  ADS  Google Scholar 

  12. Mancini, S., Man’ko, V.I., Tombesi, P.: Phys. Lett. A 213, 1 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  13. Mancini, S., Man’ko, V.I., Tombesi, P.: Found. Phys. 27, 801 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  14. Man’ko, V.I., Man’ko, O.V.: JETP 85, 430 (1997)

    Article  ADS  Google Scholar 

  15. Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., Sternheimer, D.: Lett. Math. Phys. 1, 521–530 (1977)

    Article  ADS  Google Scholar 

  16. Kontsevich, M.: Deformation quantization of Poisson manifolds. arXiv:9709040 (1997)

  17. Man’ko, O.V., Man’ko, V.I., Marmo, G.: J. Phys. A 35, 699–719 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  18. Asorey, M., Facchi, P., Man’ko, V.I., Marmo, G., Pascazio, S., Sudarshan, E.C.G.: Phys. Rev. A 77, 042115 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  19. Asorey, M., Facchi, P., Man’ko, V.I., Marmo, G., Pascazio, S., Sudarshan, E.C.G.: Physica Scripta 90, 065101 (2015)

    Article  ADS  Google Scholar 

  20. Ibort, A., Man’ko, V.I., Marmo, G., Simoni, A., Stornaiolo, C., Ventriglia, F.: Phys. Scr. 91, 4 (2016)

    Article  Google Scholar 

  21. Dodonov, V.V., Man’ko, V.I.: Invariants and correlated states of nonstationary quantum systems. In: Markov, M. A. (ed.) Invariants and the evolution of nonstationary quantum systems, Proceedings of Lebedev physics institute 183. (Nauka, Moscow 1987) 71-181, translated by Nova Science, pp 103–261. Commack, New York (1989)

  22. Man’ko, V.I., Marmo, G., Simoni, A., Stern, A., Ventriglia, F.: Phys. Lett. A 343, 4 (2005)

    Google Scholar 

  23. Mancini, S., Man’ko, O.V., Man’ko, V.I., Tombesi, P.: J. Phys. A 34, 3461 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  24. Sudarshan, E.C.G.: Phys. Lett. A 73, 4 (1979)

    Article  MathSciNet  Google Scholar 

  25. Potocek, V., Barnett, S.M.: New J. Phys. 17, 103034 (2015)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow Region, 141700, Russia

    A. A. Strakhov & V. I. Man’ko

  2. P.N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia

    V. I. Man’ko

Authors
  1. A. A. Strakhov
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  2. V. I. Man’ko
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Correspondence to A. A. Strakhov.

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Strakhov, A.A., Man’ko, V.I. Quadratic Tomography Star Product Algebra and its Classical Limit. Int J Theor Phys 58, 543–557 (2019). https://doi.org/10.1007/s10773-018-3953-6

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  • DOI: https://doi.org/10.1007/s10773-018-3953-6

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