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References
E. Schrödinger, “Über die Umkehrung der Naturgesetze”, Berlin, Sitzungsbericht 1931, 144–153
E. Schrödinger, “Sur la théorie relativiste de l'électron et l'interprétation de la mécanique quantique”, Annales de l'institut H. Poincaré 2, 289–295 (1932)
R. Fürth, “Über einige Beziehungen zwischen klassischer Statistik und Quantenmechanik”, Zeitschrift für Physik 81, 143–162 (1933)
M. Born, “Zur Quantenmechanik der Stoßvorgänge”, Zeitschrift für Physik 37, 863–867 (1926)
S. Von Neumann, “Mathematical Foundation of Quantum Mechanics”, translation by R.T. Beyer, Princeton University Press
R.P. Feynman, “Space time approach to non-relativistic quantum mechanics”, Rev. Mod. Phys. 20. 367–385 (1948)
R.P. Feynman, A.R. Hibbs, “Quantum mechanics and path integrals”, McGrawHill (1965)
C. DeWitt-Morette, A. Mahcohwani, B. Nelson, “Path Integral in Non-Relativistic Quantum Mechanics”, Phys. Rep. 50, 255–372 (1979) (and reference therein)
E. Nelson, “Dynamical theories of Brownian Motion”, Princeton University Press (1967)
E. Nelson, “Quantum Fluctuation”, Princeton. Princeton University Press (1985)
F. Guerra, “Structural aspects of stochastic mechanics and stochastic field theory”, Phys. Rep. 77, 263–312 (1981)
A. Jaffe, T. Glimm, “Quantum Physics. A Functional Integral Point of View”, Springer-Verlag (1981)
R. Azencott, H. Doss, L'equation de Schrödinger quand ħ tend vers zero. Une approche probabiliste, in “Stochastic Aspects of Classical and Quantum Systems”, Proceedings Marseille 1983, Lecture Notes in Mathematics 1109 — Springer-Verlag (1985)
M. Kac, “On some connections between Probability Theory and Differential and Integral Equations”, Proc. second Berkely Symp. (Univ. of California Press, Berkeley (1951)) pp. 189–215
K. Osterwalder, R. Schrader, “Axioms for Euclidean Green's function I, II, Comm. Math. Phys. 31, 83–112 (1973); 42, 281–305 (1975)
A.M. Chebotarev, V.P. Maslov, “Processus a sauts et leurs applications dans la mécanique quantique”, in Feynman Path Integral proceedings Marseille (1978). Lecture Notes in Physics 106, Springer Verlag (1979)
V.P. Maslov, A.M. Chebotarev, “Jump processes and their application to quantum mechanics”, Journal of Soviet Mathematics 13 (1980) 315–357 (Engl. translation)
Ph. Combe, R. Høegh-Krohn, R. Rodriguez, M. Sirugue, M. Sirugue-Collin, “Poisson Processes as Groups and Feynman Path Integrals”, Commun. Math. Phys. 77, 269–288 (1980)
see also “Feynman path integral and Poisson processes with piecewise classical paths”, J.M.P. 23, 405–411 (1982)
J. Bertrand, G. Rideau, An intrinsic approach to the evolution of quantum observables in terms of stochastic processes on phase space. In Stochastic Aspects of Classical and Quantum Systems. Lecture Notes in Mathematics, Springer-Verlag, 1985
S. Albeverio, R. Høegh-Krohn “Mathematical theory of Feynman path integrals”, Lecture Notes in Math. 523 Berlin, Heidelberg, New York Springer (1976)
E. Wigner, “On the quantum correction for thermodynamic equilibrium”, Phys. Rev. 40, 749–759 (1932)
U. Faro, “Description of States in Quantum Mechanics by density and operator techniques”, Rev. Mod. Phys. 29 (1957), 74–93
Ph. Combe, F. Guerra, R. Rodriguez, M. Sirugue, M. Sirugue-Collin, “Quantum dymanical time evolution as stochastic flows on phase space”, Physica 124A, 561–574 (1984)
S. Albeverio, Ph. Blanchard, Ph. Combe, R. Høegh-Krohn, M. Sirugue, “Local relativistic flows for quantum fields”, Comm. Math. Phys. 90, 329–351 (1983)
Ph. Combe, R. Rodriguez, M. Sirugue, M. Sirugue-Collin, “A Uniqueness Theorem for Anticommutative Relations and Commutation Relation of Quantum Spin Systems”, Comm. Math. Phys. 63, 219–235 (1978)
Ph. Combe, R. Rodriguez, M. Sirugue, M. Sirugue-Collin, A uniqueness theorem for central extensions of discrete products of cyclic groups, in “Quantum Field Algebras — Processes”, ed. L. Streit, Springer-Verlag Wien (1980)
Ph. Combe, R. Rodriguez, M. Sirugue, M. Sirugue-Collin, “On the quantization of spin systems and Fermi systems”, J.M.P. 20, 611–161 (1979)
J.E. Moyal, “Quantum Mechanics as a Stochastic Theory”, Proc. Cambridge Phis. Soc. 45, 74–93 (1949)
I.I. Gihman, A.V. Skorohod, “Stochastic Differential Equations”, Springer Verlag (1972)
See also “The Theory of Stochastic Processes III”, Springer Verlag (1979)
Ph. Blanchard, Ph. Combe, M. Sirugue, M. Sirugue-Collin, Estimate of Quantum Deviations from Classical Mechanics Using Large Deviation Results, in “Quantum Probability Applications II, Heidelberg 1984”, Lect. Notes in Math. 1136, Springer Verlag (1985)
Ph. Blanchard, M. Sirugue, “Large deviations from classical paths”. Hamiltonian flows as classical limits of quantum flows”, Comm. in Math. Phys. 101, 173.185 (1985)
Ph. Combe, R. Rodriguez, M. Sirugue and M. Sirugue-Collin, “High Temperature Behaviour of Quantum Mechanical Thermal Functionals”, R.I.M.S. Math. Sciences, Kyoto University 19, 355–365 (1983)
Ph. Combe, R. Høegh-Krohn, R. Rodriguez, M. Sirugue, M. Sirugue-Collin, “Zero mass, 2-dimensional, real time Sine-Gordon model without u.u. cut-offs”, Ann. Inst. H. Poincaré 37, 115–127 (1982)
D. Ruelle, “Statistical Mechanics, New York, Benjamin (1969)
H.P. McKean, “Stochastic Integrals”, Academic Press, New York (1969)
A.D. Ventsel, “Rough limit theorem on large deviations for Markov stochastic processes I,II,III”, Theory Prob. Application 21, 227–242 & 1976); 21, 499–512 (1976); 24, 675–692 (1979).
See also: M.I. Friedlin, A.D. Ventsel, “Random Perturbations of Dynamical Systems”, Springer-Verlag New York (1984)
D.W. Stroock, Introduction to the Theory of Large Deviations: Springer-Verlag (1984)
A.R.S. Varadhan, “Large Deviation and Application”, Courant Institute of Mathematical Sciences, New York University
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Blanchard, P., Combe, P., Sirugue, M., Sirugue-Collin, M. (1986). Jump processes in quantum theories. In: Albeverio, S., Casati, G., Merlini, D. (eds) Stochastic Processes in Classical and Quantum Systems. Lecture Notes in Physics, vol 262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540171665_56
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DOI: https://doi.org/10.1007/3540171665_56
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