Abstract
Particle motion in stochastic space, i.e., space whose coordinates consist of small, regular stochastic parts, is considered. A free particle in this space resembles a Brownian particle the motion of which is characterized by a dispersionD dependent on the universal length l. It is shown that in the first approximation in the parameter l the particle motion in an external force field is described by equations coincident in form with equations of stochastic mechanics due to Nelson, Kershow, and de la Pena-Auerbach. A method is proposed for the relativization of the scheme used to describe the processes in the stochastic space; by using this method, the equations of particle motion can be written in a covariant form.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Nelson,Phys. Rev. 150, 1079 (1966);Dynamical Theories of Brownian Motion (Princeton, N. J., 1967).
E. Nelson,J. Funct. Anal. 12, 97, 211 (1973).
F. Guerra and P. Ruggiero,Phys. Rev. Lett. 31, 1022 (1973).
T. G. Dankel,Arch. Rat. Mech. Anal. 37, 192 (1970);J. Math. Phys. 18, 253 (1977).
J. P. Caubet, Le mouvement Brownien relativiste, inLecture Notes in Mathematics, No. 559 (Heidelberg, 1976);
L. de la Pena-Auerbach,J. Math. Phys. 12, 453 (1971)
W. J. Lehr and J. L. Park,J. Math. Phys. 18, 1235 (1977)
F. Guerra and P. Ruggiero,Lett. Nuovo Cimento 23, 529 (1978).
P. Braffort and C. Tzara,C. R. Acad. Sci. Paris 239, 1779 (1954); T. W. Marshall,Proc. Roy. Soc. A 276, 475 (1963); M. Surdin,Int. J. Theor. Phys. 4(2), 117 (1971); E. Santos,Nuovo Cimento 19, 57 (1974); T. H. Boyer:Phys. Rev. D 11, 790, 809 (1975).
D. I. Blokhintsev:Fiz. Elem. Chastits At. Yad. 5, 606 (1975);Sov. J. Part. Nucl. 5, 242 (1975), and references quoted therein; M. Dineikhan and Kh. Namsrai:Theor. Math. Phys. 33, 32 (1977) (in Russian); C. Frederick,Phys. Rev. D 13, 3183 (1976).
D. I. Blokhintsev,Space and Time in the Microworld (Reidel, Dordrecht, 1973).
G. V. Efimov,Nonlocal Interactions of Quantized Fields (Nauka, Moscow, 1977) andCommun. Math. Phys. 7, 138 (1968); V. A. Alebastrov and G. V. Efimov,Commun. Math. Phys. 38, 11 (1974).
D. Kershaw,Phys. Rev. 136, B1850 (1964).
B. Skagerstam, Inst. Theor. Phys. report 75-21 Gothenburg, Sweden (1975).
J. P. Vigier,Lett. Nuovo Cim. 24, 265 (1979).
Ch. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Francisco, 1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Namsrai, K. Relativistic dynamics of stochastic particles. Found Phys 10, 353–361 (1980). https://doi.org/10.1007/BF00715078
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00715078