Skip to main content
SpringerLink
Log in

Relativistic Systems and Their Evolution in Quantum Tomography

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We propose a method of writing the relativistic equation for the probability-distribution function in the tomographic representation. The connection with the quantum-mechanical description of a zero-spin particle is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Mancini, V. I. Man'ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996); Found. Phys., 27, 801 (1997).

    Google Scholar 

  2. G. G. Amosov and V. I. Man'ko, Phys. Lett. A, 318, 287 (2003).

    Google Scholar 

  3. A. S. Arkhipov, Yu. E. Lozovik, and V. A. Sharapov, Phys. Rev. A, 69, 022116 (2004).

    Google Scholar 

  4. A. S. Arkhipov and Yu. E. Lozovik, Phys. Lett. A, 319, 217 (2003).

    Google Scholar 

  5. A. S. Arkhipov and Yu. E. Lozovik, Zh. ´ Eksp. Teor. Fiz., 125, 1 (2003).

    Google Scholar 

  6. J. Bertrand and P. Bertrand, Found. Phys., 17, 397 (1987).

    Google Scholar 

  7. K. Vogel and H. Risken, Phys. Rev. A, 40, 2847 (1989).

    Google Scholar 

  8. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett., 70, 1244 (1993).

    Google Scholar 

  9. G. M. D'Ariano, L. Maccone, and M. Paini, J. Opt. B: Quantum Semiclass. Opt., 5, 77 (2003).

    Google Scholar 

  10. S. Schiller, G. Breitenbach, S. F. Pereira, T. Muller, and J. Mlynek, Phys. Rev. Lett., 77, 2933 (1996).

    Google Scholar 

  11. D. G. Welsch, W. Vogel, and T. Opatrny, in: E. Wolf (ed.), Progress in Optics, Elsevier, Amsterdam (1999).

    Google Scholar 

  12. M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett., 72, 1137 (1994).

    Google Scholar 

  13. M. G. Raymer, D. F. McAlister, and U. Leonhardt, Phys. Rev. A, 54, 2397 (1996).

    Google Scholar 

  14. M. G. Raymer and A. C. Funk, Phys. Rev. A, 61, 015801 (2000).

    Google Scholar 

  15. J. Ashburn, R. Cline, P. van der Burgt, W. Westerveld, and J. Risley, Phys. Rev. A, 41, 2407 (1990).

    Google Scholar 

  16. O. Carnal and J. Mlynek, Phys. Rev. Lett., 66, 2689 (1991).

    Google Scholar 

  17. D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, Phys. Rev. Lett., 66, 2693 (1991).

    Google Scholar 

  18. T. J. Dunn, I. A. Walmsley, and S. Mukamel, Phys. Rev. Lett., 74, 884 (1995).

    Google Scholar 

  19. V. I. Man'ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, J. Russ. Laser Res., 24, 507 (2003); J. Opt. B: Quantum Semiclass. Opt., 6, 172 (2004); Phys. Lett. A, 327, 353 (2004).

    Google Scholar 

  20. G. G. Amosov and V. I. Man'ko, J. Russ. Laser Res., 25, 253 (2004).

    Google Scholar 

  21. M. A. Man'ko, J. Russ. Laser Res., 22, 505 (2001).

    Google Scholar 

  22. R. Fedele, S. De Nicola, M. A. Man'ko, and V. I. Man'ko, J. Russ. Laser Res., 25, 1 (2004).

    Google Scholar 

  23. L. D. Landau, Z. Phys. 45, 430 (1927).

    Google Scholar 

  24. J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932).

    Google Scholar 

  25. E. Wigner, Phys. Rev., 40, 749 (1932).

    Google Scholar 

  26. J. E. Moyal, Proc. Cambridge Phil. Soc., 45, 99 (1949).

    Google Scholar 

  27. K. Husimi, Proc. Phys. Math. Soc. Jpn, 22, 264 (1940).

    Google Scholar 

  28. E. C. G. Sudarshan, Phys. Rev. Lett., 10, 277 (1963).

    Google Scholar 

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

    Google Scholar 

  30. A. W¨unsche, J. Mod. Opt., 47, 33 (2000).

    Google Scholar 

  31. V. I. Man'ko, L. Rosa, and P. Vitale, Phys. Rev. A, 57, 3291 (1998).

    Google Scholar 

  32. V. V. Dodonov and V. I. Man'ko, Phys. Lett. A, 229, 335 (1997).

    Google Scholar 

  33. S. Weigert, Phys. Rev. Lett., 84, 802 (2000).

    Google Scholar 

  34. V. I. Man'ko and O. V. Man'ko, Zh. ´ Eksp. Teor. Phys., 85, 430 (1997).

    Google Scholar 

  35. O. V. Man'ko, V. I. Man'ko, and G. Marmo, Phys. Scr. 62, 446 (2000); J. Phys. A: Math. Gen., 35, 699 (2002).

    Google Scholar 

  36. U. Leonhardt, Phys. Rev. A, 53, 2998 (1996).

    Google Scholar 

  37. A. B. Klimov, O. V. Man'ko, V. I. Man'ko, Yu. F. Smirnov, and V. N. Tolstoy, J. Phys. A: Math. Gen., 35, 6101 (2002).

    Google Scholar 

  38. O. Castaños, R. Lòpez-Peña, M. A. Man'ko, and V. I. Man'ko, J. Phys. A: Math. Gen., 36, 4677 (2003); 37, 8529 (2004); J. Opt. B: Quantum Semiclass. Opt., 5, 227 (2003).

    Google Scholar 

  39. V. I. Manko, L. Rosa, and P. Vitale, Phys. Lett. B, 439, 328 (1998).

    Google Scholar 

  40. A. S. Arkhipov, Yu. E. Lozovik, and V. I. Man'ko, J. Russ. Laser Res., 24, 237 (2003).

    Google Scholar 

  41. A. S. Arkhipov, Yu. E. Lozovik, and V. I. Man'ko, Phys. Lett. A, 328, 419 (2004).

    Google Scholar 

  42. V. I. Man'ko and R. V. Mendes, Physica D, 145, 230 (2000).

    Google Scholar 

  43. G. R. Shin, I. Bialynicki-Birula, and J. Rafelski, Phys. Rev. A, 46, 645 (1992); I. Bialynicki-Birula, Phys. Rev. D, 49, 6920 (1994).

    Google Scholar 

  44. V. I. Tatarsky, Sov. Phys. Usp., 139, 4, 587 (1983).

    Google Scholar 

  45. H. W. Lee, Phys. Rep., 259, 147 (1995).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700, Russia

    A. S. Arkhipov

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

    V. I. Man'ko

Authors
  1. A. S. Arkhipov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Man'ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arkhipov, A.S., Man'ko, V.I. Relativistic Systems and Their Evolution in Quantum Tomography. Journal of Russian Laser Research 25, 468–476 (2004). https://doi.org/10.1023/B:JORR.0000043734.67132.96

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JORR.0000043734.67132.96

Search

Navigation