Keywords
- Vector Field
- Riemannian Manifold
- Covariant Derivative
- Stochastic Differential Equation
- Configuration Space
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References
de Angelist G.F., Jona-Lasino G., Servo M., and Zanghi N., Stochastic mechanics of a Dirac particle in two spacetime dimensions.-Journ. Phys., Ser. A, 1986, v. 19.
Belopol'skaya Ya. I. and Daletskiiyu.L., Ito equations and differential geometry.-Usp. Matem. Nauk, 1982, v. 37, No. 3 (in Russian).
Belopol'skaya Ya.I. and Daletskii Yu.L., Stochastic equations and differential geometry.-In: An analysis on manifolds and differential equations. Voronezh, 1986 (in Russian; English translation: Lect. Notes Math., 1986, v. 1214).
Bishop R.L. and Crittenden R.J., Geometry of manifolds.-Academic Press, 1964.
Daletskii Yu.L., Stochastic differential geometry.-Usp. Matem. Nauk, 1983, v. 38, No. 3 (in Russian).
Dankel T.G. (Jr.), Mechanics on manifolds and the incorporation of spin into Nelson's stochastic mechanics.-Arch. Rat. Mech. Anal., 1970, v. 37, No. 3.
Dohrn D. and Guerra F., Nelson's stochastic mechanics on Riemannian manifolds.-Lettere al Nuovo Cimento, 1978, v.22, No.4.
Dohrn D. and Guerra F., Geodesic correction to stochastic parallel displacement of tensors.-Lect. Notes Phys., 1979, v. 93.
Dohrn D., Guerra F., and Ruggiero P., Spinning particles and relativistic particles in the framework of Nelson's stochastic mechanics.-Lect. Notes Phys., 1979, v. 106.
Dombrowski P., On the geometry of tangent bundle.-Journ. reine und angew. Math., 1962, Bd. 210, Heft 1/2.
Eliasson H.I., Geometry of manifolds of maps.-Journ. Diff. Geometry, 1967, v. 1, No. 2.
Elworthy K.D., Stochastic differential equations on manifolds.-Cambridge, 1982.
Farris W.G., Spin correlation in stochastic mechanics.-Foundations of Physics, 1982, v. 12, No. 1.
Fényes I., Eine wahrscheinlichkeitstheoretische Begründung und Interpretation der Quantenmechanik.-Zeitschrift fur Physik, 1952, v. 132.
Gikhman I.I. and Skorokhod A.V., The theory of stochastic processes.-Moscow, 1975, v. 3 (in Russian).
Gliklikh Yu.E., Riemannian parallel translation in non-linear mechanics.-In: Topological and geometrical methods in mathematical physics. Voronezh, 1983 (in Russian; English translation: Lect. Notes Math., 1984,v.1108).
Gliklikh Yu.E., On Riemannian metrics possessing a Riemannian uniform atlas.-In: Differential geometry of manifolds of figures. Kaliningrad, 1985, No. 16 (in Russian).
Gliklikh Yu.E., Riemannian parallel translation, Ito integral, and stochastic equations on manifolds.-In: An analysis on manifolds and differential equations. Voronezh, 1986 (in Russian; English translation: Lect. Notes Math., 1986, v. 1214).
Guerra F. and Morato L.M., Quantization of dynamical systems and stochastic control theory.-Phys. Reviews, Ser. D, 1983, p. 1774–1786.
Guerra F. and Ruggiero P., A note on relativistic Markov processes. Lettere al Nuovo Cimento, 1978, v. 23, No. 16.
Ito K., Stochastic parallel displacement.-Lect. Notes Math., 1975, v. 451.
Ito K. Extension of stochastic integrals.-In: Proc. of Intern. Symp. SDE (Kyoto, 1976), New York, 1978.
Nelson E., Derivation of Schrödinger equation from Newtonian mechanics.-Phys. Rev., 1966, v. 150, No. 4.
Nelson E. Dynamical theories of Brownian motion. Princeton, 1967.
Nelson E. "Le mouvement brownien relativiste" by J.-P. Caubet (book review).-Bull. Amer. Math. Soc., 1979, v. 84, No. 1.
Nelson E., Quantum fluctuations.-Princeton, 1985.
Vershik A.M. and Faddeev L.D., Differential geometry and Lagrangian mechanics with constraints.-Dokl. Akad. Nauk SSSR, 1972, v. 202, No. 3 (in Russian).
Vershik A.M. and Faddeev L.D., Lagrangian mechanics in an invariant representation.-In: Problems in theoretical physics. Leningrad, 1975, No. 2 (in Russian).
Vershik A.M. Classical and non-classical dynamics with constraints. In: Geometry and topology in global non-linear problems. Voronezh, 1984 (in Russian; English translation: Lect. Notes Math., 1984, v. 1108).
Yasue K., Quantum mechanics and stochastic control theory.-J. Math. Phys., 1981, v. 22, No. 5.
Yasue K., Stochastic calculus of variations.-J. Funct. Anal., 1981, v. 41.
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Gliklikh, Y.E. (1988). Geometrical aspects of nelson's stochastic quantization. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A. (eds) Global Analysis — Studies and Applications III. Lecture Notes in Mathematics, vol 1334. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080432
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DOI: https://doi.org/10.1007/BFb0080432
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