Feynman et les mathématiques
Annales mathématiques Blaise Pascal, Tome 3 (1996) no. 1, pp. 211-226. 
@article{AMBP_1996__3_1_211_0,
     author = {Zambrini, Jean-Claude},
     title = {Feynman et les math\'ematiques},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {211--226},
     publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal},
     volume = {3},
     number = {1},
     year = {1996},
     mrnumber = {1397333},
     zbl = {0864.60001},
     language = {fr},
     url = {http://www.numdam.org/item/AMBP_1996__3_1_211_0/}
}
TY  - JOUR
AU  - Zambrini, Jean-Claude
TI  - Feynman et les mathématiques
JO  - Annales mathématiques Blaise Pascal
PY  - 1996
SP  - 211
EP  - 226
VL  - 3
IS  - 1
PB  - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
UR  - http://www.numdam.org/item/AMBP_1996__3_1_211_0/
LA  - fr
ID  - AMBP_1996__3_1_211_0
ER  - 
%0 Journal Article
%A Zambrini, Jean-Claude
%T Feynman et les mathématiques
%J Annales mathématiques Blaise Pascal
%D 1996
%P 211-226
%V 3
%N 1
%I Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
%U http://www.numdam.org/item/AMBP_1996__3_1_211_0/
%G fr
%F AMBP_1996__3_1_211_0
Zambrini, Jean-Claude. Feynman et les mathématiques. Annales mathématiques Blaise Pascal, Tome 3 (1996) no. 1, pp. 211-226. http://www.numdam.org/item/AMBP_1996__3_1_211_0/

[0] R. Descartes, Discours de la méthode, Flammarion, Paris.

[1] J. Von Neumann, Mathematical foundations of Quantum Mechanics, Princeton Univ. Press, Princeton N. J. (1955). | MR | Zbl

[2] E. Schrödinger, Quantization as a problem of proper values, part I,II, Annalen der Physik (4), vol 79 (1926).

[3] (1) V. Arnold, Méthodes mathématiques de la mécanique classique, Editions Mir, Moscou (1976). (2) R. Abraham,J. Marsden, Foundations of Mechanics, Benjamin (1978). | MR | Zbl

[4] R. Feynman,A. Hibbs, Quantum mechanics and path integrals, Mc. Graw-Hill (1965). | Zbl

[5] R.H. Cameron, A family of integrals serving to connect the Wiener and Feynman integrals, J. Math. Physics 39,126 (1960). | MR | Zbl

[6] B. Simon, Functional integration and quantum physics, Acad .Press, N. Y. (1979). | MR | Zbl

[7] W.H. Fleming,H.M. Soner, Controlled Markov processes and viscosity solutions, Springer-Verlag, New York (1993). | MR | Zbl

[8] N.V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Reidel, Dordrecht (1987). | Zbl

[9] P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equation, part I, Comm. PDE 8, 1101 (1983; | MR | Zbl

P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equation, part II, Comm. PDE 8, 1229 (1983). | MR | Zbl

[10] N. Ikeda,S. Watanabe, Stochastic differential equations and diffusion processes, North - Holland Kodansha, N. Y., (1981). | MR | Zbl

[11] A.D. Wentzell, A course in the theory of stochastic processes, Mc. Graw-Hill, N. Y. (1981). | Zbl

[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). | Numdam | MR | Zbl

[13] E. Nelson, Dynamical theories of Brownian motion, Princeton Univ. Press, Princeton, N.J. (1967). | MR | Zbl

[14] (1) A. Beurling, Annals of Math. (2), 72, n. 1, 189 (1960). (2) B. Jamison, Z. Wahrsch. Gebiete 30, 65 (1974). | MR | Zbl

[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).

[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. | MR

[17] P. Malliavin, Stochastic calculus of variations and hypoelliptic operators, in Proc. Int. Symp. SDE, Kyoto 1976, Kinokuniya, Tokyo (1978). | Zbl

[18] E. Cartan, Leçons sur les invariants intégraux, Hermann, Paris (1971). | MR | Zbl

[19] A.B. Cruzeiro, J.C. Zambrinien préparation.