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The physics of stochastic electrodynamics

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Il Nuovo Cimento B (1971-1996)

Summary

The problem of the electron immersed in the random zeropoint radiation field and described by the stochastic Abraham-Lorentz equation is analysed from a new point of view. First an approximate treatment of the (statistically) stationary motion of this system is performed by using a local linearization procedure applicable to nonlinear periodic problems. Our treatment leads to a (quantum) condition on the mean kinetic energy of the stationary states. The random field is thus seen to have a selective and stabilizing effect on the dynamics. The results are applied to the hydrogen atom and other problems and the old quantum rules are briefly discussed in the light of this quantization mechanism. In the second part we develop a formalism to describe the stationary regime of this stochastic system. Using the canonical properties of the vacuum field amplitudes, we derive symplectic relations for the particle variablesx, p; in addition, a canonical treatment of the system allows us to derive the equations of evolution. A Hilbert-space formalism arises as a possible tool for the mathematical treatment (inx orp space) and it is shown to lead to the usual description of quantum mechanics.

Riassunto

Si analizza da un nuovo punto di vista il problema dell'elettrone immerso in un campo di radiazioni random nel punto zero e descritto dall'equazione stochastica di Abraham-Lorentz. Prima si esegue una trattazione approssimativa del moto (statisticamente) stazionario di questo sistema, usando una procedura di linearizzazione locale applicabile a problemi periodici non lineari. La nostra trattazione porta ad una condizione (quantistica) sull'energia cinetica media degli stati stazionari. Il campo casuale appare cosí avere un effetto selettivo e stabilizzante sulla dinamica. I risultati sono applicati all'atomo d'idrogeno e ad altri problemi e le vecchie regole quantistiche sono discusse in breve alla luce del meccanismo di quantizzazione. Nella seconda parte si sviluppa un formalismo per descrivere il regime stazionario di questo sistema stocastico. Usando le proprietà canoniche delle ampiezze di campo nel vuoto, si derivano relazioni simplettiche per le variabili delle particellex, p; inoltre un trattamento canonico del sistema ci permette di derivare le equazioni di evoluzione. Un formalismo dello spazio di Hilbert si presenta come possibile strumento per una trattazione matematica (nello spaziox op) e si mostra come esso porta alla solita descrizione della meccanica quantistica.

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References

  1. A. A. Sokolov andV. S. Tumanov:JETP (Moscow),30, 802 (1956).

    Google Scholar 

  2. R. Schiller andH. Tesser:Phys. Rev. A,3, 2035 (1971).

    Article  ADS  Google Scholar 

  3. E. Santos:J. Math. Phys. (N. Y.),15, 1954 (1974).

    Article  ADS  MATH  Google Scholar 

  4. P. W. Milonni:Phys. Lett. A,82, 225 (1981); see alsoAm. J. Phys.,52, 340 (1984) for a more elementary account.

    Article  MathSciNet  ADS  Google Scholar 

  5. This idea was made explicit for the first time byN. S. Kalitsin:JETP (Moscow),25, 407 (1953), and later rediscovered and developed byBraffort and co-workers (6)M. Spighel andC. Tzara:C. R. Acad. Sci.,239, 157 (1954). andMarshali) (7)Proc. R. Soc. London, Ser. A,276, 475 (1963);, among others. A general review on SED can be found in ref. (8) inStochastic Processes Applied to Physics and Other Related Fields, edited byB. Gómez et al. (World Scientific Publ. Co., Singapore, 1983); and shorter, more specific ones in ref. (9-13)T. H. Boyer:Phys. Rev. D,11, 790 (1975).T. A. Brody:Rev. Mex. Fis.,29, 461 (1983).

    Google Scholar 

  6. P. Braffort, M. Spighel andC. Tzara:C. R. Acad. Sci.,239, 157 (1954).

    MATH  Google Scholar 

  7. T. W. Marshall:Proc. R. Soc. London, Ser. A,276, 475 (1963);Proc. Cambridge Philos. Soc.,61, 537 (1965).

    Article  ADS  Google Scholar 

  8. L. de la Peña: inStochastic Processes Applied to Physics and Other Related Fields, edited byB. Gómez et al. (World Scientific Publ. Co., Singapore, 1983).

    Google Scholar 

  9. T. H. Boyer:Phys. Rev. D,11, 790 (1975).

    Article  ADS  Google Scholar 

  10. T. H. Boyer: inFoundations of Radiation Theory and Quantum Electrodynamics, edited byA. O. Barut (Plenum Press, New York, N. Y., 1980).

    Google Scholar 

  11. E. Santos:Stochastic theory vs. quantum theory, preprint GIFT, Universidad de Santander (1975).

  12. P. Claverie andS. Diner:Isr. J. Chem.,19, 54 (1980).

    Article  Google Scholar 

  13. T. A. Brody:Rev. Mex. Fis.,29, 461 (1983).

    MathSciNet  MATH  Google Scholar 

  14. Provisional accounts are contained in the internal communications:A. M. Cetto andL. de la Peña: preprint IFUNAM 83-04 (September 1983); preprint IFUNAM 84-05 (May 1984).

  15. E. Santos:Nuovo Cimento B,19, 57 (1974).

    Article  ADS  Google Scholar 

  16. L. de la Peña andA. M. Cetto:J. Math. Phys. (N. Y.),20, 469 (1979).

    Article  ADS  Google Scholar 

  17. L. de la Peña andA. M. Cetto:Rev. Mex. Fis.,25, 1 (1976).

    Google Scholar 

  18. P. Claverie, L. Pesquera andF. Soto:Phys. Lett. A,80, 113 (1980);P. Claverie andF. Soto:J. Math. Phys. (N. Y.),23, 753 (1982);L. Pesquera andP. Claverie;J. Math. Phys. (N. Y.),23, 1315 (1982).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. T. H. Boyer:Phys. Rev. D,13, 2832 (1976);Phys. Rev. A,18, 1228 (1978).

    Article  ADS  Google Scholar 

  20. S. M. Moore andJ. A. Ramírez:Nuovo Cimento B,54, 275 (1981).

    Article  Google Scholar 

  21. See,e.g.,P. Hänggi,F. Marchesoni andP. Grigolini:Z. Phys. B,56, 333 (1984).

    Article  ADS  MATH  Google Scholar 

  22. T. W. Marshall:Nuovo Cimento,38, 206 (1965).

    Article  Google Scholar 

  23. T. H. Boyer:Ann. Phys. (N. Y.),56, 474 (1970).

    Article  ADS  Google Scholar 

  24. T. H. Boyer:Phys. Rev. A,21, 66 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  25. L. de la Peña andA. Jáuregui:Found. Phys.,12, 441 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  26. T. H. Boyer:Phys. Rev. D,29, 1096 (1984). For previous attempts, seePhys. Rev.,186, 1304 (1969);O. Theimer:Phys. Rev. D,4, 1597 (1971).

    Article  ADS  Google Scholar 

  27. A similar proposal was presented byE. Santos:Lett. Nuovo Cimento,4, 497 (1972).

    Article  Google Scholar 

  28. N. Krylov andN. N. Bogoliubov:Introduction to Nonlinear Mechanics (Princeton University Press, Princeton, N. J., 1943).

    Google Scholar 

  29. C. Hayashi:Nonlinear Oscillations in Physical Systems (McGraw-Hill, New York, N. Y., 1964), Chapt. 2.

    MATH  Google Scholar 

  30. F. M. Fernández, A. M. Mesón andE. A. Castro:Kinam,5, 21 (1983).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica della I, Università, 00185, Roma

    L. de la Peña & A. M. Cetto

  2. Instituto de Física, UNAM, ap. Postal 20-364, 01000, México, D.F.

    L. de la Peña & A. M. Cetto

Authors
  1. L. de la Peña
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  2. A. M. Cetto
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de la Peña, L., Cetto, A.M. The physics of stochastic electrodynamics. Nuov Cim B 92, 189–217 (1986). https://doi.org/10.1007/BF02732647

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  • DOI: https://doi.org/10.1007/BF02732647

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