Skip to main content
Log in

Stochastic quantization at finite temperature

  • Published:
La Rivista del Nuovo Cimento (1978-1999) Aims and scope

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

Access this article

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

Instant access to the full article PDF.

References

  1. S. Chandrasekhar:Rev. Mod. Phys.,15, 1 (1943).

    Article  MathSciNet  ADS  Google Scholar 

  2. P. C. Hohenberg andB. I. Halperin:Rev. Mod. Phys.,49, 435 (1977).

    Article  ADS  Google Scholar 

  3. J. D. Gunton andM. Droz:Introduction to the Theory of Metastable and Unstable States, Lecture Notes in Physics, Vol.183 (Springer-Verlag, Berlin, 1983).

    Book  Google Scholar 

  4. H. Haken:Synergetics (Springer-Verlag, Berlin, 1978).

    Book  Google Scholar 

  5. E. Nelson:Phys. Rev.,150, 1079 (1966);Dynamical theories of Brownian Motion (Princeton University Press, Princeton, N.J., 1967);Quantum Fluctuations (Princeton University Press, Princeton, N.J., 1984).

    Article  ADS  Google Scholar 

  6. M. Jammer:The Philosophy of Quantum Mechanics (J. Wiley and Sons, New York, N. Y., 1974).

    Google Scholar 

  7. I. Féynes:Z. Phys.,132, 81 (1952).

    Article  Google Scholar 

  8. G. Jona-Lasinio, F. Martinelli andE. Scoppola:Phys. Rep.,77, 313 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  9. H. B. Callen andT. A. Welton:Phys. Rev.,83, 34 (1951).

    Article  MathSciNet  ADS  Google Scholar 

  10. G. E. Uhlenbeck andL. S. Ornstein:Phys. Rev.,36, 823 (1930).

    Article  ADS  Google Scholar 

  11. R. Kubo:J. Phys. Jpn.,12, 570 (1957).

    Article  MathSciNet  ADS  Google Scholar 

  12. L. Landau andE. Lifchitz:Physique statistique (MIR, Moscou, 1967), Chapt. XII.

    Google Scholar 

  13. F. Guerra:Phys. Rep.,77, 263 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  14. F. Guerra andL. Morato:Phys. Rev. D,27, 1774 (1983);E. Nelson:Quantum Fluctuations (Princeton University Press, Princeton, N.J., 1984).

    Article  MathSciNet  ADS  Google Scholar 

  15. D. ter Haar:Problems in Quantum Mechanics (London, 1975), p. 169.

  16. F. Guerra andM. I. Loffredo:Lett. Nuovo Cimento,30, 81 (1981).

    Article  MathSciNet  Google Scholar 

  17. R. J. Glauber:Phys. Rev.,131, 2766 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  18. H. Haken:Rev. Mod. Phys.,47, 67 (1975);R. W. Hasse:Rep. Prog. Phys.,41, 1027 (1978);J. Messer:Acta Phys. Austriaca,50, 75 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  19. G. W. Ford, M. Kac andP. Mazur:J. Math. Phys. (N. Y.),6, 504 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  20. M. D. Kostin:J. Chem. Phys.,57, 3589 (1972).

    Article  ADS  Google Scholar 

  21. F. Haake: inQuantum Statistics in Optics and Solid-State Physics, edited byG. Hohler andE. A. Niekisch (Springer-Verlag, Berlin, 1973), p. 98;J. Messer andB. Baumgartner:Z. Phys. B,32, 103 (1978).

    Chapter  Google Scholar 

  22. H. Dekker:Phys. Rep.,80, 1 (1981);W. Stocker andK. Albrecht:Ann. Phys. (N. Y.),117, 436 (1979);P. Caldirola andL. Lugiato:Physica (Utrecht) A,116, 248 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  23. K. K. Kan andJ. J. Griffin:Phys. Lett. B,50, 241 (1974).

    Article  ADS  Google Scholar 

  24. B. K. Skagerstam:J. Math. Phys. (N. Y.),18, 308 (1977);K. Yasue:Ann. Phys. (N. Y.),114, 479 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  25. P. Ruggiero andM. Zannetti:Phys. Rev. Lett.,48, 963 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  26. L. Landau andL. Lifchitz:Physique statistique (MIR, Moscou, 1967), Chapt. III.

    Google Scholar 

  27. R. Figari, P. Rugguero andM. Zannetti:J. Phys. A,17, L419 (1984).

    Article  ADS  Google Scholar 

  28. R. Benguria andM. Kac:Phys. Rev. Lett.,46, 1 (1981);F. DePasquale, P. Ruggiero andM. Zannetti:J. Phys. A,17, 1489 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  29. P. Ullersma:Physica (Utrecht),32, 27 (1966).

    Article  MathSciNet  ADS  Google Scholar 

  30. As general references seeS. K. Ma:Modern Theory of Critical Phenomena (W. A. Benjamin, Reading, Mass., 1976);D. J. Amit:Field Theory Renormalization Group and Critical Pehnomena (McGraw-Hill, New York, N. Y., 1978);C. Domb andM. S. Green, Editors:Phase Transitions and Critical Phenomena (Academic Press, New York, N. Y., 1974).

    Google Scholar 

  31. J. A. Hertz:Phys. Rev. B,14, 1165 (1976).

    Article  ADS  Google Scholar 

  32. M. Suzuki:Prog. Theor. Phys.,56, 1454 (1976);R. Jullien:Can. J. Phys.,59, 605 (1981).

    Article  ADS  Google Scholar 

  33. R. Opperman andH. Thomas:Z. Phys. B,22, 387 (1975);R. Morf, T. Schneider andE. Stoll:Phys. Rev. B,16, 462 (1977);H. Bilz, A. Bussmann, G. Benedek, H. Büttner andD. Strauch:Ferroelectrics,25, 339 (1980).

    Article  ADS  Google Scholar 

  34. U. T. Höchli, H. E. Weibl andL. A. Boatner:Phys. Rev. Lett.,39, 1158 (1977);K. A. Müller andH. Burkard:Phys. Rev. B,19, 3593 (1979);U. T. Höchli:Ferroelectrics,35, 17 (1981).

    Article  ADS  Google Scholar 

  35. P. Ruggiero andM. Zannetti:Phys. Rev. B,27, 3001 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  36. S. K. Ma:Rev. Mod. Phys.,45, 589 (1973).

    Article  ADS  Google Scholar 

  37. For an alternative interpretation based on stochastic mechanics, which does not involve the concept of dimensional cross-over, seeP. Rugglero andM. Zannetti:Phys. Rev. Lett.,47, 1231 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  38. This point is discussed in detail in ref. [35].

    Article  MathSciNet  ADS  Google Scholar 

  39. Y. Imry andS. K. Ma:Phys. Rev. Lett.,35, 1399 (1975);G. Parisi andN. Sourlas:Phys. Rev. Lett.,43, 744 (1979).

    Article  ADS  Google Scholar 

  40. F. de Pasquale, P. Ruggiero andM. Zannetti:Phys. Rev. B,30, 2695 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  41. A. Aharony, Y. Gefen andY. Shapir:J. Phys. C,15, 673 (1982);D. Boyanovsky andJ. L. Cardy:Phys. Rev. B,27, 5557 (1983).

    Article  ADS  Google Scholar 

  42. E. Wong:Stochastic Processes in Information and Dynamical Systems (McGraw-Hill, New York, N. Y., 1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruggiero, P., Zannetti, M. Stochastic quantization at finite temperature. Riv. Nuovo Cim. 8, 1–47 (1985). https://doi.org/10.1007/BF02724343

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02724343

Navigation