Jump processes and diffusions in relativistic stochastic mechanics
Annales de l'I.H.P. Physique théorique, Volume 53 (1990) no. 3, p. 301-317
@article{AIHPA_1990__53_3_301_0,
     author = {de Angelis, G. F. and Serva, M.},
     title = {Jump processes and diffusions in relativistic stochastic mechanics},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {53},
     number = {3},
     year = {1990},
     pages = {301-317},
     zbl = {0711.60083},
     mrnumber = {1084882},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1990__53_3_301_0}
}
de Angelis, G. F.; Serva, M. Jump processes and diffusions in relativistic stochastic mechanics. Annales de l'I.H.P. Physique théorique, Volume 53 (1990) no. 3, pp. 301-317. http://www.numdam.org/item/AIHPA_1990__53_3_301_0/

[1] E. Nelson, Derivation of the Schrödinger Equation from Newtonian Mechanics, Phys. Rev., Vol. 150, 1966, p. 1079.

[2] E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967. | MR 214150 | Zbl 0165.58502

[3] E. Nelson, Quantum Fluctuations, Princeton University Press, Princeton, 1985. | MR 783254 | Zbl 0563.60001

[4] F. Guerra, Structural Aspect of Stochastic Mechanics and Stochastic Field Theory, Phys. Rep., Vol. 77, 1981, p. 263. | MR 639032

[5] F. Guerra and P. Ruggiero, A Note on Relativistic Markov Processes, Lett. Nuovo Cimento, Vol. 23, 1978, p. 529.

[6] F. Guerra and D. Dohrn, Compatibility Between the Brownian Metric and the Kinetic Metric in Nelson Stochastic Quantization, Phys. Rev. D, Vol. 31, 1985, p. 2521. | MR 790461

[7] G.F. De Angelis, G. Jona-Lasinio, M. Serva and N. Zanghi, Stochastic Mechanics of a Dirac Particle in Two Space-Dimensions, J. Phys. A: Math. Gen., Vol. 19, 1986, p. 865. | MR 841174 | Zbl 0615.60076

[8] M. Serva, Relativistic Stochastic Processes Associated to Klein-Gordon Equation, Ann. Inst. Henri Poincaré, Vol. 49, 1988, p. 415. | Numdam | MR 988945 | Zbl 0659.60095

[9] R. Marra and M. Serva, Variational Principles for Relativistic Stochastic Mechanics, preprint BiBoS, Bielefeld, 1989.

[10] G.F. De Angelis, Stochastic Mechanics of Relativistic Spinless Particle, J. Math. Phys., Vol. 31, 1990, 1408. | MR 1054330 | Zbl 0712.46041

[11] T.D. Newton and E.P. Wigner, Localized States for Elementary Systems, Rev. Mod. Phys., Vol. 20, 1948, p. 367. | Zbl 0036.26704

[12] T. Ichinose and H. Tamura, Imaginary-Time Path Integral for a Relativistic Spinless Particle in an Electromagnetic Field, Commun. Math. Phys., Vol. 105, 1986, p. 239. | MR 849207 | Zbl 0606.60060

[13] T. Ichinose, The Nonrelativistic Limit Problem for a Relativistic Spinless Particle in an Electromagnetic Field, J. Funct. Analysis, Vol. 73, 1987, p. 233. | MR 899650 | Zbl 0618.46063

[14] K. Ito and H.P. Mckeanjr., Diffusions Processes and their Sample Paths, Springer-Verlag, Berlin, Heidelberg, New York, 1974. | Zbl 0285.60063

[15] G. Jona-Lasinio, F. Martinelli and E. Scoppola, New Approach to the Semiclassical Limit of Quantum Mechanics, Commun. Math. Phys., Vol. 80, 1981, p. 223. | MR 623159 | Zbl 0483.60094

[16] D. Bakry, La propriété de sous-harmonicité des diffusions dans les variétés, in Séminaire de Probabilité XXII, Lect. Notes Math., No. 1321, Springer-Verlag, 1988. | Numdam | MR 960507 | Zbl 0653.58043

[17] R. Carmona, Path integrals for relativistic Schrödinger operators, in Lect. Notes Phys., Vol. 345, Springer-Verlag, 1988. | MR 1037317 | Zbl 0712.35069

[18] R. Carmona, W.C. Masters and B. Simon, Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions, J. Funct. Analysis, Vol. 91, 1990, p. 117. | MR 1054115 | Zbl 0716.35006