Advertisement

Russian Journal of Mathematical Physics

, Volume 20, Issue 2, pp 254–256 | Cite as

Quantum probability and Levy Laplacians

  • B. O. Volkov
Short Communications

Abstract

The formula Δ L = limɛ→0st∥<ɛ b s b t dsdt for the Levy Laplacian is obtained, where b t stands for an annihilation process. The formula is extended to some generalizations of the Levy Laplacian.

Keywords

Quantum Probability Annihilation Process Real Separable Hilbert Space White Noise Analysis Quantum Stochastic Calculus 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Accardi, P. Gibilisco, and I. V. Volovich, “Yang-Mills Gauge Fields as Harmonic Functions for the Levy Laplacians,” Russ. J. Math. Phys. 2(2), 235–250 (1994).MathSciNetzbMATHGoogle Scholar
  2. 2.
    L. Leandre and I. V. Volovich,“The Stochastic Levy Laplacian and Yang-Mills Equation on Manifolds,” Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4(2), 151–172 (2001).MathSciNetCrossRefGoogle Scholar
  3. 3.
    B. O. Volkov, “Lévy Laplacian and the Gauge Fields,” Infin. Dimens. Anal. Quantum Probab. Relat. Top. 15(4), 1250027 [19 pages] (2012).CrossRefGoogle Scholar
  4. 4.
    L. Accardi and O. G. Smolyanov, “Classical and Nonclassical Lévy Laplacians,” Dokl. Akad. Nauk 76(3), 801–805, (2007).MathSciNetzbMATHGoogle Scholar
  5. 5.
    L. Accardi and O. G. Smolyanov, “Generalized Lévy Laplacians and Cesaro Means,” Dokl. Akad. Nauk. 79(1), 90–93 (2009).MathSciNetzbMATHGoogle Scholar
  6. 6.
    L. Accardi and O. G. Smolyanov, ”Representations of Lévy Laplacians and Related Semigroups and Harmonic Functions,” Dokl. Akad. Nauk 65(3), 356–362 (2002).MathSciNetzbMATHGoogle Scholar
  7. 7.
    F. Gomez and O. G. Smolyanov, “Modified Lévy Laplacians,” Russ. J. Math. Phys. 15(1), 45–50 (2008).MathSciNetzbMATHGoogle Scholar
  8. 8.
    N. Obata, White Noise Calculus and Fock Space, Lect. Notes in Math. 1577 (Springer, Berlin, 1994).zbMATHGoogle Scholar
  9. 9.
    L. Accardi, Y.-G. Lu, and I. V. Volovich, “Nonlinear Extensions of Classical and Quantum Stochastic Calculus and Essentially Infinite Dimensional Analysis,” in: Probability Towards 2000, Ed. by L. Accardi, C. C. Heyde, Lecture Notes in Statistics 128, pp. 1–33 (1998).CrossRefGoogle Scholar
  10. 10.
    H.-H. Kuo, White Noise Distribution Theory (CRC Press, Boca Raton, FL, 1996).zbMATHGoogle Scholar
  11. 11.
    N. Obata, “Quadratic Quantum White Noises and Lévy Laplacian,” Nonlinear Anal. 47(4), 2437–2448 (2001).MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    L. Accardi, U. C. Ji, and K. Saitô, “Exotic Laplacians and Derivatives of White Noise,” Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14(1), 1–14 (2011).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia

Personalised recommendations