Advertisement

Stochastic Quantization and Gauge Fixing in Gauge Theories

  • E. Seiler
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 26/1984)

Abstract

These lectures were supposed to focus on a specific non-compact lattice gauge model with a peculiar “stochastic” gauge fixing invented by Zwanziger. But to put this model into perspective I find it appropriate to widen the scope of these lectures somewhat.

Keywords

Polyakov Loop Imaginary Time Ground State Wave Function Stochastic Mechanic Stochastic Quantization 
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.
    Ph. Blanchard, these proceedings.Google Scholar
  2. 2.
    L. Streit, these proceedings.Google Scholar
  3. 3.
    P. Zoller, these proceedings.Google Scholar
  4. 4.
    E. Nelson, Phys. Rev. 150 (1966) 1079; Dynamical Theories of Brownian Motion (Princeton University Press, 1967); “Connection Between Brownian Motion and Quantum Mechanics”, in Lecture Notes in Physics, vol. 100 (Springer-Verlag, Berlin-Heidelberg-New York, 1979) (Einstein Symposium Berlin).CrossRefADSGoogle Scholar
  5. 5.
    G. Jona-Lasinio, “Stochastic Processes and Quantum Mechanics”, talk given at the Colloque en I’Honneur de L. Schwartz, Ecole Polytechnique, June 1983, to appear in Asterisque.Google Scholar
  6. 6.
    C. de Witt-Morette and D. Elworthy, Phys. Rep. 77 (1981).Google Scholar
  7. 7.
    F. Guerra and P. Ruggiero, Lett. Nuov. Cim. 31 (1973) 1022.Google Scholar
  8. 8.
    F. Guerra, Phys. Rep. 11 (1981) 263.CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    B. Simon, Functional Integration in Quantum Physics (Academic Press, New York-San Francisco-London, 1979).Google Scholar
  10. 10.
    G. Parisi and Y.S. Wu, Scientia Sinica 24 (1981) 483.MathSciNetGoogle Scholar
  11. 11.
    E. Gozzi, Phys. Lett. 129B (1983) 432, (Err. 134B (1983) 477); Phys. Lett. 130B (1983) 83; Phys. Rev. D28 (1983) 1922; “The Onsager’s Principle of Microscopic Reversibility and Supersymmetry”, CCNY-HEP-83/16;ADSMathSciNetGoogle Scholar
  12. R. Kirschner, “Quantization by Stochastic Relaxation Processes and Supersymmetry”, KMU-HEP 84–01.Google Scholar
  13. 12.
    G. Parisi and N. Sourlas, Nucl. Phys. B206 (1982) 321; Phys. Rev. Lett. 43 (1979) 744.CrossRefADSMathSciNetGoogle Scholar
  14. 13.
    P. Walters, Introduction to Ergodic Theory (Springer- Verlag, Berlin-Heidelberg-New York, 1982).CrossRefMATHGoogle Scholar
  15. 14.
    A. Guha and S.C. Lee, Phys. Rev. D27 (1982) 2412; Phys. Lett. 134B (1984) 216.ADSMathSciNetGoogle Scholar
  16. 15.
    D. Zwanziger, Nucl. Phys. B192 (1981) 259; Phys. Lett. 114B (1982) 337; Nucl. Phys. B209 (1982) 336.CrossRefADSMathSciNetGoogle Scholar
  17. 16.
    S. Helgasson, Differential Geometry and Symmetric Spaces (Academic Press, New York-San Francisco-London, 1962), Chapter X, Prop. 2.1.Google Scholar
  18. 17.
    N.D. Hari Dass, P.G. Lauwers and A. Patkos, Phys. Lett. 124B (1983) 387; Phys. Lett. 130B (1983) 292.ADSMathSciNetGoogle Scholar
  19. 18.
    L. Baulieu and D. Zwanziger, Nucl. Phys. B193 (1981) 163.CrossRefADSMathSciNetGoogle Scholar
  20. 19.
    I.M. Singer, Comm. Math. Phys. 60 (1978) 7CrossRefMATHADSMathSciNetGoogle Scholar
  21. O. Babelon and C.-M. Viallet, Phys. Lett. 85B (1979) 246.ADSMathSciNetGoogle Scholar
  22. 20.
    M. Creutz, I. Muzinich, T. Tudron, Phys. Rev. D19 (1979) 531.ADSGoogle Scholar
  23. 21.
    A. Chodos and V. Moncrief, J. Math. Phys. D19 (1980) 364.CrossRefADSMathSciNetGoogle Scholar
  24. 22.
    H. Flanders, Differential Forms with Applications to the Physical Sciences (Academic Press, New York-London, 1963).MATHGoogle Scholar
  25. 23.
    I.C. Gohberg and M.G. Krein, Introduction to the Theory of Non-selfadjoint Operators (American Mathematical Society Translations, Providence, R.I., 1969).Google Scholar
  26. 24.
    E. Seller, I.O. Stamatescu and D. Zwanziger, “Monte Carlo Simulations of Non-Compact QCD with Stochastic Gauge Fixing”, Nucl. Phys. B, in print.Google Scholar
  27. 25.
    E. Seller, I.O. Stamatescu and D. Zwanziger, “Numerical Evidence for a Barrier at the Gribov Horizon”, Nucl. Phys. B, in print.Google Scholar
  28. 26.
    I.O. Stamatescu, U. Wolff and D. Zwanziger, Nucl. Phys. B225[FS9] (1983) 377.CrossRefADSGoogle Scholar
  29. 27.
    A. Patrascioiu, E. Seller and I.O. Stamatescu, Phys. Lett. 107B (1981) 364.ADSGoogle Scholar
  30. 28.
    F. Guerra and R. Marra, “Discrete Stochastic Variational Principles ana Quantum Mechanics”, preprint Università di Roma, 1983.Google Scholar
  31. 29.
    H.P. McKean, Stochastic Integrals (Academic Press, New York-San Francisco-London 19 69);MATHGoogle Scholar
  32. N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes (North Holland Publishing Co., Amsterdam-Oxford-New York, 1981).MATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • E. Seiler
    • 1
  1. 1.Max-Planck-Institut für Physik und Astrophysik Werner-Heisenberg-Institut für PhysikMunichFed. Rep. Germany

Personalised recommendations