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Numeri di Clifford ed equazioni del mesone

  • C. Salvetti
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Riassunto

A. Proca eG. Juvet hanno applicato l’algoritmo cliffordiano rispettivamente alle equazioni diDirac e a quelle del campo elettromagnetico. Nel presente articolo le proprietà dei numeri diClifford vengono applicate alla teoria del mesone. Si mostra che le diverse equazioni del campo mesonico possono raccogliersi in un’unica equazione, particolarmente semplice ed espressiva, qualora si rinunci alla ordinaria rappresentazione tridimensionale o a quella relativistica tetradimensionale, per passare a una più generale descrizione in un continuo cliffordiano pentadimensionaleS5. I risultati di un precedente articolo dell’A. sulle proprietà degli operatori cliffordiani inS5 vengono utilizzati per dedurre una nuova forma assai generale per i potenziali da cui possono farsi derivare le grandezze che descrivono il campo mesonico e per istituirne le equazioni. Si mostra come l’algoritmo impiegato permetta di dedurre la hamiltoniana e il teorema diPoynting relativo al campo mesonico. Infine dopo avere detotto le leggi integrali del mesone inS5 anch’esse assai semplici e significative, si cerca di dare una interpretazione fisica alla quinta coordinata.

Summary

Clifford’s algebra is applied to transcribe the meson field equations in a five-dimensional continuum.

It is shown how in such space the equations that are usually employed to describe the meson field can be re-united in a particularly simple single one which is valid both in vacuum and in polarizable media (that is in presence of nucleons): in this last case, the here developed five-dimensional treatment permits to take into account both electric and magnetic moments. Briefly, the introduction of a fifth dimension permits to operate on meson field with the same simplicity that caracterizes the standard treatment of the electromagnetic field in the customary cronotops of special relativity theory. The most general expression of meson field potential is also derived and with it the equations to which it obeys.

In addition to this, Poynting’s theorem and meson hamiltonian are deduced, by carrying out the calculations on meson field equations in the five-dimensional continuum on the same lines usually followed for the electromagnetic field in four-dimensional space of the special relativity theory. After that a particularly simple and significant integral expression of meson field equations is given. Finally in an attempt to clarify the physical meaning to the fifth dimension, it is shown as being essentially connected with the particle rest mass. The extra coordinatex5 represents the length of gededesic which are described by the particle in its motion in the four-dimensional continuum of the special relativity theory («proper time»). The momentum conjugate tox5 appears to be μ0c0=rest mass of the particle).

It seem that the t o conjugate variablesx5 and μ0c satifsfy to an uncertainty relation.

References

  1. (1).
    C. Salvetti: «Rend. Ist. Lomb. Sc. lett.»,78, 347 (1945).MathSciNetGoogle Scholar
  2. (2).
    Th. Kaluza; «Sitz. Ber. Preuss. Akad. Wiss.», 966 (1921).Google Scholar
  3. (3).
    O. Klein: «Zts. f. Phys.»,37, 895 (1926).ADSCrossRefGoogle Scholar
  4. (4).
    O. Klein: «Zts. f. Phys.»,46, 188 (1927).ADSCrossRefGoogle Scholar
  5. (5).
    F. Hund: «Zts. f. Phys.»,118, 426 (1941).ADSCrossRefGoogle Scholar
  6. (6).
    P. Caldirola: «Nuovo Cimento»,19, 25 (1942);19, 300 (1942) (Err. corr.).CrossRefGoogle Scholar
  7. (7).
    A. Pais: «Physica»,9, 267 (1942).MathSciNetADSCrossRefGoogle Scholar
  8. (8).
    H. A. Bethe: «Phys. Rev.»,57, 260 (1940).ADSCrossRefGoogle Scholar
  9. (9).
    A. Proca: «Journ. de Phys.»,1-VII, 233 (1930).Google Scholar
  10. (10).
    D. I. Iwanenko eA. Sokolow: «Journ. of Phys. U.S.S.R.»,3, 56 (1940).Google Scholar
  11. (11).
    P. Caldirola: «Rend. Acc. It.», serie 7a,1, 19 (1939).MathSciNetGoogle Scholar
  12. (12).
    A. Proca: «C. R.»,186, 739 e 1097 (1928).Google Scholar

Copyright information

© Società Italiana di Fisica 1946

Authors and Affiliations

  • C. Salvetti
    • 1
  1. 1.Istituto di Fisica dell’Università di MilanoMilanoItalia

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