@article{AIHPA_1997__67_3_297_0, author = {Thieullen, M. and Zambrini, J. C.}, title = {Probability and quantum symmetries. {I.} {The} theorem of {Noether} in {Schr\"odinger's} euclidean quantum mechanics}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {297--338}, publisher = {Gauthier-Villars}, volume = {67}, number = {3}, year = {1997}, mrnumber = {1472821}, zbl = {0897.60062}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1997__67_3_297_0/} }
TY - JOUR AU - Thieullen, M. AU - Zambrini, J. C. TI - Probability and quantum symmetries. I. The theorem of Noether in Schrödinger's euclidean quantum mechanics JO - Annales de l'I.H.P. Physique théorique PY - 1997 SP - 297 EP - 338 VL - 67 IS - 3 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1997__67_3_297_0/ LA - en ID - AIHPA_1997__67_3_297_0 ER -
%0 Journal Article %A Thieullen, M. %A Zambrini, J. C. %T Probability and quantum symmetries. I. The theorem of Noether in Schrödinger's euclidean quantum mechanics %J Annales de l'I.H.P. Physique théorique %D 1997 %P 297-338 %V 67 %N 3 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1997__67_3_297_0/ %G en %F AIHPA_1997__67_3_297_0
Thieullen, M.; Zambrini, J. C. Probability and quantum symmetries. I. The theorem of Noether in Schrödinger's euclidean quantum mechanics. Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 3, pp. 297-338. http://archive.numdam.org/item/AIHPA_1997__67_3_297_0/
[1] Méthodes mathématiques de la mécanique classique, Ed. Mir, Moscou, 1976. | MR | Zbl
,[2] Commande Optimale, Ed. Mir, Moscou, 1982. | MR
, and ,[3] Quantum Mechanics and path integrals, Mc Graw - Hill, N. Y., 1965. | Zbl
and ,[4] Functional Integration and Quantum Physics, Acad. Press, N. Y., 1979. | MR | Zbl
,[5] Stochastic Differential equations and Diffusion Processes, 2nd ed., North Holland, Amsterdam, 1989. | MR | Zbl
and ,[6] On some connections between probability theory and differential and integral equations, Proc. of the 2nd, Berkeley Symp. on Prob. and Statistics, J. Newman Ed., Univ. of California Press, Berkeley, 1951. | MR | Zbl
,[7] J. Math. Physics, Vol. 39, 1960, p. 126. | Zbl
,[8] Leçons sur les invariants intégraux, Hermann, Paris, 1922. | MR
,[9] a) J. Math. Physics, Vol. 27, 1986, p. 2307. b) , and , Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 49, 1989, p. 259. | MR
,[10] Quantum fluctuations, Princeton Series in Physics, P. U. Press, 1985. | MR | Zbl
,[11] An alternative starting point for Euclidean field theory: Euclidean Quantum Mechanics, IXth International Congress of Mathematical Physics, Swansea (U.K.), Adam Hilger, N. Y., 1989, p. 260. | MR
,[12] Malliavin Calculus and Euclidean Quantum Mechanics. I. Functional Calculus, J. of Funct. Anal., Vol. 96, 1991, 1, p. 62. | MR | Zbl
and ,[13] Field Theory. A modern primer, Benjamin Cummings Publ., Reading, Mass., 1981. | MR
,[14] a) Trans. Amer. M. S., No. 277, 1984, p. 1. b) and , Controlled Markov Processes and Viscosity Solutions, Springer, 1993. | MR
and ,[15] Annals of Physics, Vol. 194, 1989, p. 336. | MR
,[16] The mathematical framework of Euclidean Quantum Mechanics. An outline in "Stochastic Analysis and Applications", Ed. A. B. Cruzeiro and J. C. Zambrini, No. 26, 1991, Birkhäuser, Boston. | MR | Zbl
and ,[17] Quantum Mechanics I, Springer-Verlag, 1989. | Zbl
and ,[18] Dynamical Theories of Brownian Motion, Princeton Univ. Press, N. J., 1967. | MR | Zbl
,[19] a) Calculus of Variations, Prentice-Hall, N.J., 1963. b) and , Classical and Quantum Dynamics, Springer-Verlag, 1994. | MR
and ,[20] a) Symmetry groups and their applications, Academic Press, N. Y., 1972. b) , Applications of Lie groups to differential equations, Springer-Verlag, N. Y., 1986. | MR | Zbl
Jr,[21] Bull. Soc. Math. de France, Vol. 85, 1957, p. 431. | Numdam | MR | Zbl
,[22] a) J. of Math. Phys., Vol. 33, 1992, No. 9, p. 3050. b) , Potential Analysis, Vol. 2, p. 349, 1993. | Zbl
,[23] Canonical transformations for diffusions, C.R. Acad. Sc. Paris, T. 321, Série I, 1995, pp. 339-344. | MR | Zbl
and ,[24] Act. Math., Vol. 161, 1988, p. 243. | Zbl
,[25] Symmetries in the Stochastic Calculus of Variations, to appear in Prob. Theory Related Fields. | MR | Zbl
and ,[26] a) Ann. Inst. H. Poincaré, Vol. 2, 1932, p. 269. b) , Sur les liaisons entre les grandeurs aléatoires, Mathematikerkongr, Zurich, Band 1, 1932. c) and , Gebiete, Vol. 30, 1974, p. 65. | JFM | Numdam | MR | Zbl
,[27] Prob. Theory Related Fields, No. 97, 1993, p. 231. | MR
,[28] Stochastic calculus of variations and hypo-elliptic operators, Proc. Int. Symp. SDE Kyoto, 1976, 1978, Kinokuniya, Tokyo. | Zbl
,[29] Markov processes, Springer-Verlag, Berlin, 1965.
,[30] Malliavin Calculus and Euclidean Quantum Mechanics, II, J. of Funct. Analysis, Vol. 130, No. 2, 1995, p. 450. | MR | Zbl
and ,[31] From Quantum Physics to Probability Theory and back, in "Chaos - the interplay between Stochastic and Deterministic behaviour", Springer lecture Notes in Physics, No. 457, GARBACZEWSKI et al., eds., Springer, Berlin, 1995. | MR | Zbl
,[32] Calculus of Variations and Quantum Probability in Lect. Notes in Control and Info., 1988, No. 121, p. 173, N. Y. | MR
,[33] Reciprocal diffusions in flat space, Prob. Theory Related fields, No. 107, 1997, p. 243. | MR | Zbl
,[34] Stochastic mechanics of reciprocal diffusions, J. Math. Physics, Vol. 37, 1996, p. 769. | MR | Zbl
and ,[35] Nonlinear elliptic and parabolic equations of the second order, Reidel, Dodrecht, 1987.
,[36] Probability and quantum symmetries, II. The Theorem of Noether in quantum mechanics.
, and ,[37] Conserved quantities and symmetry for stochastic dynamical systems., Phys. Letters A, 1994, No. 195, p. 185. | MR | Zbl
,[38] Stochastic analysis, Grund. der Math. Wiss., Vol. 313, Springer, 1997. | Zbl
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