Abstract
We study the connection between operator ordering schemes and thec-number formulations of quantum mechanics, which are based on generating functionals and functional integrals. We show by explicit construction that different operator ordering schemes are related to different functional and functional integral formulations of quantum mechanics. The results of these considerations are applied to classical non-linear stochastic dynamics by using the formal analogy between the Fokker-Planck equation and the Schrödinger equation.
Similar content being viewed by others
References
Lurié, D.: Particles and Fields. New York: Interscience 1968
Fried, H.M.: Functional Methods and Models in Quantum Field Theory. Cambridge: MIT Press 1972
Abers, E.S., Lee, B.W.: Phys. Rep.9 C, 1 (1973)
Katz, A.: Classical Mechanics, Quantum Mechanics, Field Theory. New York: Academic Press 1972
Rosen, G.: Formulations of Classical and Quantum Dynamical Theory. New York: Academic Press 1969
Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. New York: McGraw-Hill 1965
Cohen, L.: J. Math. Phys.11, 3296 (1970)
Testa, F.J.: J. Math. Phys.12, 1471 (1971)
Berezin, F.A.: Theor. Math. Phys.6, 141 (1971)
Mayes, I.W., Dowker, J.S.: J. Math. Phys.14, 434 (1973)
Mizrahi, M.M.: J. Math. Phys.16, 2201 (1975)
Fanelli, R.: J. Math. Phys.17, 490 (1976)
Cohen, L.: J. Math. Phys.17, 597 (1976)
Dowker, J.S.: J. Math. Phys.17, 1873 (1976)
Kubo, R., Matsuo, K., Kitahara, K.: J. Stat. Phys.9, 51 (1973)
Graham, R.: Springer Tracts in Modern Physics66, 1 (1973)
Graham, R., in Fluctuations, Instabilities and Phase Transitions (ed. Riste, T.). New York: Plenum Press 1976
Horsthemke, W., Bach, A.: Z. Physik B22, 189 (1975)
Haken, H.: Z. Physik B24, 321 (1976)
Graham, R.: Z. Physik B26, 281 (1977)
Kitahara, K., Metiu, H.: J. Stat. Phys.15, 141 (1976)
Yahata, H.: Progr. Theor. Phys.51, 2003 (1974); Progr. Theor. Phys.52, 871 (1974)
Janssen, H.K.: Z. Physik B23, 377 (1976)
Bausch, R., Janssen, H.K., Wagner, H.: Z. Physik B24, 113 (1976)
Martin, P.C., Siggia, E.D., Rose, H.A.: Phys. Rev. A8, 423 (1973)
Cohen, L.: J. Math. Phys.7, 781 (1966)
Cahill, K.E., Glauber, R.J.: Phys. Rev.177, 1857 (1969)
Agarwal, G.S., Wolf, E.: Phys. Rev. D2, 2161, 2187, 2206 (1970)
Schmutz, M.: Nuovo Cimento25 B, 337 (1975)
Arthurs, A.M., Ed.: Functional Integration and Its Applications. Oxford: Clarendon Press 1975
Albeverio, S.A., Høegh-Krohn, R.J.: Lecture Notes in Mathematics523 (1976)
Wilson, K.G., Kogut, J.: Phys. Rep.12 C, 75 (1974)
Zwanzig, R., in Statistical Mechanics (eds. Rice, S.A., Freed, KF., Light, J.C.). Chicago: University of Chicago Press 1972
Kawasaki, K.: Progr. Theor. Phys.51, 1064 (1974); Progr. Theor. Phys.52, 84, 1527 (1974)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Leschke, H., Schmutz, M. Operator orderings and functional formulations of quantum and stochastic dynamics. Z Physik B 27, 85–94 (1977). https://doi.org/10.1007/BF01315509
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01315509