A stochastic scheme for constructing solutions of the Schrödinger equations
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 32 (1980) no. 4, pp. 327-341.
@article{AIHPA_1980__32_4_327_0,
     author = {Dewitt-Morette, C. and Elworthy, K. D. and Nelson, B. L. and Sammelman, G. S.},
     title = {A stochastic scheme for constructing solutions of the {Schr\"odinger} equations},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {327--341},
     publisher = {Gauthier-Villars},
     volume = {32},
     number = {4},
     year = {1980},
     mrnumber = {594632},
     zbl = {0446.60045},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1980__32_4_327_0/}
}
TY  - JOUR
AU  - Dewitt-Morette, C.
AU  - Elworthy, K. D.
AU  - Nelson, B. L.
AU  - Sammelman, G. S.
TI  - A stochastic scheme for constructing solutions of the Schrödinger equations
JO  - Annales de l'institut Henri Poincaré. Section A, Physique Théorique
PY  - 1980
SP  - 327
EP  - 341
VL  - 32
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1980__32_4_327_0/
LA  - en
ID  - AIHPA_1980__32_4_327_0
ER  - 
%0 Journal Article
%A Dewitt-Morette, C.
%A Elworthy, K. D.
%A Nelson, B. L.
%A Sammelman, G. S.
%T A stochastic scheme for constructing solutions of the Schrödinger equations
%J Annales de l'institut Henri Poincaré. Section A, Physique Théorique
%D 1980
%P 327-341
%V 32
%N 4
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1980__32_4_327_0/
%G en
%F AIHPA_1980__32_4_327_0
Dewitt-Morette, C.; Elworthy, K. D.; Nelson, B. L.; Sammelman, G. S. A stochastic scheme for constructing solutions of the Schrödinger equations. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 32 (1980) no. 4, pp. 327-341. http://www.numdam.org/item/AIHPA_1980__32_4_327_0/

H. Airault, Subordination de processus dans Ie fibré tangent et formes harmoniques, C. R. Acad. Sc. Paris, t. 282, Sér. A, 1976, p. 1311-1314. | MR | Zbl

S.J. Avis and C.J. Isham, Lorentz gauge invariant vacuum functionals for quantized spinor fields in non-simply connected space-times. Preprint Imperial College, London SW7 2BZ, 1979. | MR

J.M.C. Clark, An introduction to stochastic differential equations on manifolds, Geometric Methods in Systems Theory (D. Q. Mayne, R. W. Brockett, eds.), Reidel, Holland, 1973. | Zbl

B.S. De Witt, Dynamical theory in curved spaces. I. A review of the classical and quantum action principles, Rev. Mod. Phys., t. 29, 1957, p. 337-397. | MR | Zbl

B.S. De Witt, C.F. Hart and C.J. Isham, Topology and quantum field theory. To appear in the Schwinger Festschrift.

C. De Witt-Morette, A. Maheshwari and B. Nelson, Path integration in non-relativistic mechanics, Physics Reports, t. 50, 1979, p. 257-372.

C. De Witt-Morette and K.D. Elworthy, Stochastic differential equations. Lecture notes and problems, Preprint of the Center for Relativity, University of Texas, Austin, TX 78712, 1979.

J. Dollard and C. Friedman, Product integration, Addison-Wesley, 1979. | MR

J.S. Dowker, Quantum mechanics and field theory on multiply connected and on homogeneous spaces, J. Phys. A. Gen. Phys., t. 5, 1972, p. 936-943. | MR

J. Eells and K.D. Elworthy, Stochastic Dynamical Systems, in Control theory and topics in functional analysis, vol. III, International Atomic Energy Agency, Vienna, 1976, p. 179-185. | MR | Zbl

K.D. Elworthy, Stochastic differential equations on manifolds. Notes based on seminars given by J. Eells and K. D. Elworthy, available from the Department of Mathematics, University of Warwick, Coventry CV4 7AL, and references therein, 1978.

K.D. Elworthy and A. Truman, Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation on riemannian manifolds. In preparation, 1979. | Zbl

W. Garczynski, On alternative ways of including an external electromagnetic field, Bull. Acad. Polonaise Sciences, t. XXI, 1973, p. 355-358.

M.G.G. Laidlaw, Ph. D. Thesis, University of North Carolina, 1971.

M.G.G. Laidlaw and C.M. Dewitt, Feynman functional integrals for systems of indistinguishable particles, Phys. Rev., t. D 3, 1971, p. 1375-1377.

D.W. Mclaughlin and L.S. Schulman, Path integrals in curved spaces, J. Math. Phys., t. 12, 1971, p. 2520-2524. | MR

C. Morette, On the definition and approximation of Feynnman's path integrals, Phys. Rev., t. 81, 1951, p. 848-852. | MR | Zbl

B.L. Nelson and B. Sheeks, Path integration for velocity dependent potentials, Preprint of the Center for Relativity, University of Texas, Austin, TX 78712, 1979.

W. Pauli, Asugewahlte Kapitel aus Der Feldquantisierung, Gehalten an Der E. T. H. in Zürich, 1950-1951. Reprinted in Pauli Lectures in Physics, Ed. C. P. Enz, MIT Press, 1952.

H.R. Petry, Exotic spinors in superconductivity, J. Math. Phys., t. 20, 1979, p. 231-240. | MR

M.A. Pinsky, Stochastic riemannian geometry, Probabilistic analysis and related topics, t. 1, 1978, p. 199-236. | MR | Zbl

L.S. Schulman, A path integral for spin, Phys. Rev., t. 176, 1968, p. 1558-1567. | MR

L.S. Schulman, Green's function for an electron in a lattice, Phys. Rev., t. 188, 1969, p. 1139-1142.

B. Simon, Functional integration and quantum physics, Academic Press, 1979. | MR | Zbl

N. Steenrod, The topology of fibre bundles, Princeton University Press, 1951. | MR | Zbl

A. Truman, Classical mechanics, the diffusion (heat) equation and the Schrödinger equation, J. Math. Phys., t. 18, 1977, p. 2308-2315. | MR | Zbl

S.K. Wong, Field and particle equations for the classical Yang-Mills field and particles with isotropic spin, Nuovo Cimento, t. 65, 1970, p. 689-694.

C.N. Yang and R.L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev., t. 96, 1954, p. 191-195. | MR

S.T. Yau, On the heat kernel of a complete riemannian manifold, J. Math. pures et appl., t. 57, 1978, p. 191-207. | MR | Zbl