Jump processes and diffusions in relativistic stochastic mechanics

G. F. de Angelis; M. Serva

Annales de l'I.H.P. Physique théorique (1990)

  • Volume: 53, Issue: 3, page 301-317
  • ISSN: 0246-0211

How to cite

top

de Angelis, G. F., and Serva, M.. "Jump processes and diffusions in relativistic stochastic mechanics." Annales de l'I.H.P. Physique théorique 53.3 (1990): 301-317. <http://eudml.org/doc/76506>.

@article{deAngelis1990,
author = {de Angelis, G. F., Serva, M.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {relativistic quantum spinless particles; Klein-Gordon propagator; jump Markov processes; Hamiltonian semigroup},
language = {eng},
number = {3},
pages = {301-317},
publisher = {Gauthier-Villars},
title = {Jump processes and diffusions in relativistic stochastic mechanics},
url = {http://eudml.org/doc/76506},
volume = {53},
year = {1990},
}

TY - JOUR
AU - de Angelis, G. F.
AU - Serva, M.
TI - Jump processes and diffusions in relativistic stochastic mechanics
JO - Annales de l'I.H.P. Physique théorique
PY - 1990
PB - Gauthier-Villars
VL - 53
IS - 3
SP - 301
EP - 317
LA - eng
KW - relativistic quantum spinless particles; Klein-Gordon propagator; jump Markov processes; Hamiltonian semigroup
UR - http://eudml.org/doc/76506
ER -

References

top
  1. [1] E. Nelson, Derivation of the Schrödinger Equation from Newtonian Mechanics, Phys. Rev., Vol. 150, 1966, p. 1079. 
  2. [2] E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967. Zbl0165.58502MR214150
  3. [3] E. Nelson, Quantum Fluctuations, Princeton University Press, Princeton, 1985. Zbl0563.60001MR783254
  4. [4] F. Guerra, Structural Aspect of Stochastic Mechanics and Stochastic Field Theory, Phys. Rep., Vol. 77, 1981, p. 263. MR639032
  5. [5] F. Guerra and P. Ruggiero, A Note on Relativistic Markov Processes, Lett. Nuovo Cimento, Vol. 23, 1978, p. 529. 
  6. [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. MR790461
  7. [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. Zbl0615.60076MR841174
  8. [8] M. Serva, Relativistic Stochastic Processes Associated to Klein-Gordon Equation, Ann. Inst. Henri Poincaré, Vol. 49, 1988, p. 415. Zbl0659.60095MR988945
  9. [9] R. Marra and M. Serva, Variational Principles for Relativistic Stochastic Mechanics, preprint BiBoS, Bielefeld, 1989. Zbl0701.60106
  10. [10] G.F. De Angelis, Stochastic Mechanics of Relativistic Spinless Particle, J. Math. Phys., Vol. 31, 1990, 1408. Zbl0712.46041MR1054330
  11. [11] T.D. Newton and E.P. Wigner, Localized States for Elementary Systems, Rev. Mod. Phys., Vol. 20, 1948, p. 367. Zbl0036.26704
  12. [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. Zbl0606.60060MR849207
  13. [13] T. Ichinose, The Nonrelativistic Limit Problem for a Relativistic Spinless Particle in an Electromagnetic Field, J. Funct. Analysis, Vol. 73, 1987, p. 233. Zbl0618.46063MR899650
  14. [14] K. Ito and H.P. McKeanJr., Diffusions Processes and their Sample Paths, Springer-Verlag, Berlin, Heidelberg, New York, 1974. Zbl0285.60063
  15. [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. Zbl0483.60094MR623159
  16. [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. Zbl0653.58043MR960507
  17. [17] R. Carmona, Path integrals for relativistic Schrödinger operators, in Lect. Notes Phys., Vol. 345, Springer-Verlag, 1988. Zbl0712.35069MR1037317
  18. [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. Zbl0716.35006MR1054115

NotesEmbed ?

top

You must be logged in to post comments.