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Stochastic Description of Supersymmetric Fields with Values in A Manifold

  • Zbigniew Haba
Part of the NATO ASI Series book series (NSSB, volume 144)

Abstract

The mathematical problem of the (imaginary time) quantum mechanics of a particle moving in a Euclidean space can be considered as a problem from the theory of diffusion processes. The generator of the diffusion process coincides (up to a similarity transformation [1]) with the Hamiltonian of quantum mechanics. The diffusion process can be defined as well by a stochastic equation [2]. The stochastic equation describes the diffusion process as a time evolution of a Brownian particle in a force field. Some forces (like the gravitational one), have a geometrical origin. We wish to suggest in this lecture that the time evolution of some (quantum) Euclidean fields is like a free (geodesic) motion on a curved manifold.

Keywords

Brownian Particle Stochastic Equation Conformal Supergravi Fermi Field Supersymmetric Quantum Mechanic 
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.

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References

  1. 1.
    F. Guerra, P. Ruggiero, Phys. Rev.Lett. 31, 1022 (1973)ADSCrossRefGoogle Scholar
  2. 1a.
    H. Ezawa, J. Klauder, L.A. Shepp, Ann.Phys. 88, 588 (1974)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 1b.
    S. Albeverio, R. Hoegh-Krohn, L. Streit, J.Math.Phys.18, 907 (1977) A. Truman, these ProceedingsMathSciNetADSMATHCrossRefGoogle Scholar
  4. 2.
    N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland, 1981MATHGoogle Scholar
  5. 2a.
    K.D. Elworthy, Stochastic Differential Equations on Manifolds Cambridge, 1982Google Scholar
  6. 3.
    P. Malliavin, J. Funct. Anal. 17, 274(1974)MathSciNetMATHCrossRefGoogle Scholar
  7. 4.
    E. Witten, J.Diff.Geom.17,661 (1982)MathSciNetMATHGoogle Scholar
  8. 5.
    Z. Haba, J.Phys.A18, L347 (1985)MathSciNetADSGoogle Scholar
  9. 5a.
    BiBoS-Bielefeld preprint No.18, 1985Google Scholar
  10. 6.
    Z. Haba, in Lect. Notes in Physics, Ascona 1985Google Scholar
  11. 7.
    M. van den Berg, J.T. Lewis, Bull.Lond.Math.Soc.17,144(1985)Google Scholar
  12. 8.
    G. Moore, P. Nelson, Phys.Rev.Lett.53,1519 (1984)MathSciNetADSCrossRefGoogle Scholar
  13. 9.
    L. Nirenberg, J.Diff.Geom.6,561 (1972)MathSciNetMATHGoogle Scholar
  14. 10.
    Y. Rozanov, BiBoS-Bielefeld preprint No.23,1985Google Scholar
  15. 11.
    H. Nicolai, Phys.Lett.89B,341(1980),Google Scholar
  16. 11a.
    H. Nicolai, Phys.Lett.117B,408(1982)MathSciNetGoogle Scholar
  17. 12.
    C. Barnett, R.F. Streater, I.F. Wilde, J.Funct.Anal.48,172(1982)MathSciNetGoogle Scholar
  18. 13.
    Z. Haba, in preparationGoogle Scholar
  19. 14.
    Z. Haba, J.Phys.A18,L957(1985)Google Scholar
  20. 15.
    V. de Alfaro, S. Fubini, G. Furlan, G. Veneziano, Nucl.Phys.2551(1985)Google Scholar
  21. 16.
    S. Albeverio, these ProceedingsGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Zbigniew Haba
    • 1
  1. 1.Inst. of Theor. Phys.University of WrocławPoland

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