Feynman et les mathématiques

Jean-Claude Zambrini

Annales mathématiques Blaise Pascal (1996)

  • Volume: 3, Issue: 1, page 211-226
  • ISSN: 1259-1734

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Zambrini, Jean-Claude. "Feynman et les mathématiques." Annales mathématiques Blaise Pascal 3.1 (1996): 211-226. <http://eudml.org/doc/79149>.

@article{Zambrini1996,
author = {Zambrini, Jean-Claude},
journal = {Annales mathématiques Blaise Pascal},
keywords = {quantization method for elementary classical systems via path integrals; probabilistic conservation laws},
language = {fre},
number = {1},
pages = {211-226},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {Feynman et les mathématiques},
url = {http://eudml.org/doc/79149},
volume = {3},
year = {1996},
}

TY - JOUR
AU - Zambrini, Jean-Claude
TI - Feynman et les mathématiques
JO - Annales mathématiques Blaise Pascal
PY - 1996
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 3
IS - 1
SP - 211
EP - 226
LA - fre
KW - quantization method for elementary classical systems via path integrals; probabilistic conservation laws
UR - http://eudml.org/doc/79149
ER -

References

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  1. [0] R. Descartes, Discours de la méthode, Flammarion, Paris. Zbl27.0009.02
  2. [1] J. Von Neumann, Mathematical foundations of Quantum Mechanics, Princeton Univ. Press, Princeton N. J. (1955). Zbl0064.21503MR66944
  3. [2] E. Schrödinger, Quantization as a problem of proper values, part I,II, Annalen der Physik (4), vol 79 (1926). 
  4. [3] (1) V. Arnold, Méthodes mathématiques de la mécanique classique, Editions Mir, Moscou (1976). (2) R. Abraham, J. Marsden, Foundations of Mechanics, Benjamin (1978). Zbl0385.70001MR474391
  5. [4] R. Feynman, A. Hibbs, Quantum mechanics and path integrals, Mc. Graw-Hill (1965). Zbl0176.54902
  6. [5] R.H. Cameron, A family of integrals serving to connect the Wiener and Feynman integrals, J. Math. Physics39,126 (1960). Zbl0096.06901MR127776
  7. [6] B. Simon, Functional integration and quantum physics, Acad .Press, N. Y. (1979). Zbl0434.28013MR544188
  8. [7] W.H. Fleming, H.M. Soner, Controlled Markov processes and viscosity solutions, Springer-Verlag, New York (1993). Zbl0773.60070MR1199811
  9. [8] N.V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Reidel, Dordrecht (1987). Zbl0619.35004
  10. [9] P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equation, part I, Comm. PDE8, 1101 (1983; Zbl0716.49022MR709164
  11. P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equation, part II, Comm. PDE8, 1229 (1983). Zbl0716.49023MR709162
  12. [10] N. Ikeda, S. Watanabe, Stochastic differential equations and diffusion processes, North - HollandKodansha, N. Y., (1981). Zbl0495.60005MR637061
  13. [11] A.D. Wentzell, A course in the theory of stochastic processes, Mc. Graw-Hill, N. Y. (1981). Zbl0502.60001
  14. [12] (1) J.C. Zambrini, J. Math. Phys.27, 2307 (1986). (2) S. Albeverio, K. Yasue, J.C. Zambrini, Ann.Inst. Henri Poincaré, Phys. Th.49 (3), 259 (1989). Zbl0687.60091MR854761
  15. [13] E. Nelson, Dynamical theories of Brownian motion, Princeton Univ. Press, Princeton, N.J. (1967). Zbl0165.58502MR214150
  16. [14] (1) A. Beurling, Annals of Math. (2), 72, n. 1, 189 (1960). (2) B. Jamison, Z. Wahrsch. Gebiete30, 65 (1974). Zbl0091.13001MR125424
  17. [15] A.B. Cruzeiro, J.C. Zambrini, Journ. of Funct. Anal. vol 96, n.1, 62 (1991); Journ. of Funct.Anal. vol 130, n.2, 450 (1995). A.B. Cruzeiro, Z. Haba, J.C. Zambrini, Bernstein diffusions and Euclidean quantum field theory, in Progr. in Prob. vol 36, 77, E. Bolthausen, F. Russo Eds, Birkhäuser (1993). Zbl0835.60036
  18. [16] M. Thieullen, J.C. Zambrini, Symmetries in stochastic calculus of variations, preprint Univ. Paris VI; The theorem of Noether in Schrödinger's Euclidean quantum mechanics, preprint Institut Mittag-Leffler. Zbl0897.60062MR1440139
  19. [17] P. Malliavin, Stochastic calculus of variations and hypoelliptic operators, in Proc. Int. Symp. SDE, Kyoto 1976, Kinokuniya, Tokyo (1978). Zbl0411.60060
  20. [18] E. Cartan, Leçons sur les invariants intégraux, Hermann, Paris (1971). Zbl0212.12501MR355764
  21. [19] A.B. Cruzeiro, J.C. Zambrinien préparation. 

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