References
S. Chandrasekhar:Rev. Mod. Phys.,15, 1 (1943).
P. C. Hohenberg andB. I. Halperin:Rev. Mod. Phys.,49, 435 (1977).
J. D. Gunton andM. Droz:Introduction to the Theory of Metastable and Unstable States, Lecture Notes in Physics, Vol.183 (Springer-Verlag, Berlin, 1983).
H. Haken:Synergetics (Springer-Verlag, Berlin, 1978).
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).
M. Jammer:The Philosophy of Quantum Mechanics (J. Wiley and Sons, New York, N. Y., 1974).
I. Féynes:Z. Phys.,132, 81 (1952).
G. Jona-Lasinio, F. Martinelli andE. Scoppola:Phys. Rep.,77, 313 (1981).
H. B. Callen andT. A. Welton:Phys. Rev.,83, 34 (1951).
G. E. Uhlenbeck andL. S. Ornstein:Phys. Rev.,36, 823 (1930).
R. Kubo:J. Phys. Jpn.,12, 570 (1957).
L. Landau andE. Lifchitz:Physique statistique (MIR, Moscou, 1967), Chapt. XII.
F. Guerra:Phys. Rep.,77, 263 (1981).
F. Guerra andL. Morato:Phys. Rev. D,27, 1774 (1983);E. Nelson:Quantum Fluctuations (Princeton University Press, Princeton, N.J., 1984).
D. ter Haar:Problems in Quantum Mechanics (London, 1975), p. 169.
F. Guerra andM. I. Loffredo:Lett. Nuovo Cimento,30, 81 (1981).
R. J. Glauber:Phys. Rev.,131, 2766 (1963).
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).
G. W. Ford, M. Kac andP. Mazur:J. Math. Phys. (N. Y.),6, 504 (1965).
M. D. Kostin:J. Chem. Phys.,57, 3589 (1972).
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).
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).
K. K. Kan andJ. J. Griffin:Phys. Lett. B,50, 241 (1974).
B. K. Skagerstam:J. Math. Phys. (N. Y.),18, 308 (1977);K. Yasue:Ann. Phys. (N. Y.),114, 479 (1978).
P. Ruggiero andM. Zannetti:Phys. Rev. Lett.,48, 963 (1982).
L. Landau andL. Lifchitz:Physique statistique (MIR, Moscou, 1967), Chapt. III.
R. Figari, P. Rugguero andM. Zannetti:J. Phys. A,17, L419 (1984).
R. Benguria andM. Kac:Phys. Rev. Lett.,46, 1 (1981);F. DePasquale, P. Ruggiero andM. Zannetti:J. Phys. A,17, 1489 (1984).
P. Ullersma:Physica (Utrecht),32, 27 (1966).
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).
J. A. Hertz:Phys. Rev. B,14, 1165 (1976).
M. Suzuki:Prog. Theor. Phys.,56, 1454 (1976);R. Jullien:Can. J. Phys.,59, 605 (1981).
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).
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).
P. Ruggiero andM. Zannetti:Phys. Rev. B,27, 3001 (1983).
S. K. Ma:Rev. Mod. Phys.,45, 589 (1973).
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).
This point is discussed in detail in ref. [35].
Y. Imry andS. K. Ma:Phys. Rev. Lett.,35, 1399 (1975);G. Parisi andN. Sourlas:Phys. Rev. Lett.,43, 744 (1979).
F. de Pasquale, P. Ruggiero andM. Zannetti:Phys. Rev. B,30, 2695 (1984).
A. Aharony, Y. Gefen andY. Shapir:J. Phys. C,15, 673 (1982);D. Boyanovsky andJ. L. Cardy:Phys. Rev. B,27, 5557 (1983).
E. Wong:Stochastic Processes in Information and Dynamical Systems (McGraw-Hill, New York, N. Y., 1971).
Author information
Authors and Affiliations
Rights 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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02724343