Il Nuovo Cimento B (1971-1996)

, Volume 61, Issue 2, pp 220–228 | Cite as

Some physical aspects induced by the internal variable in the theory of fields in Finsler spaces

  • S. Ikeda


Some physical aspects underlying the theory of fields in Finsler spaces are considered. Since the internal variable (y) is associated with each point (x), some special conditions must be imposed on the Finslerian structure, that is to say some special Finsler spaces must be chosen in order to take out they-dependent features. In this paper, tangent space and local Minkowski space are taken up.

Некоторые физические аспекты, связанные с внутренней переменной в теории поля в пространствах финслера


Рассматриваются некоторые физические аспекты, возникающие в теории полей в пространствах финслера. Так как внутренняя переменная (y) связана с каждой точкой (x), то на структуру финслериана должны быть наложены некоторые специальные условия. Следовательно, необходимо выбрать некоторые специальные пространства финслера, чтобы получить зависящие отy структуры. В этой статье выбираются тангенциальное пространство и локальное пространство Минковского.


Si considerano alcuni aspetti fisici che stanno alla base della teoria dei campi negli spazi di Finsler. Poiché la variabile interna (y) è associata con ogni punto (x), alcune condizioni speciali devono essere imposte alla struttura finsleriana, cioè alcuni spazi di Finsler speciali devono essere scelti in modo da eliminare i comportamentiy-dipendenti. In questo lavoro ci si occupa dello spazio tangente e dello spazio di Minkowski locale.


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  1. (1).
    J. I. Horváth:Suppl. Nuovo Cimento,9, 444 (1958);Y. Takano:Prog. Theor. Phys.,40, 1159 (1968).CrossRefMATHGoogle Scholar
  2. (2).
    J. I. Horváth:Acta Phys. Chem. Szeged,7, 3 (1961).Google Scholar
  3. (3).
    E. Cartan:Les espaces de Finsler (Paris, 1934);H. Rund:The Differential Geometry of Finsler Spaces (Berlin, 1959).Google Scholar
  4. (4).
    M. Matsumoto:Foundation of Finsler Geometry and Special Finsler Spaces (Berlin, 1977).Google Scholar
  5. (5).
    In order to obtainy as a function ofx, integrability conditions with respect toN λκ must be satisfied, so that one kind of torsionR λ μ κ (A.7) vanishes in this case.Google Scholar
  6. (6).
    G. Randers:Phys. Rev.,59, 195 (1941).MathSciNetADSCrossRefMATHGoogle Scholar
  7. (7).
    M. Matsumoto:Tensor,24, 29 (1972);C. Shibata, H. Shimada, M. Azuma andH. Yasuda:Tensor,31, 219 (1977).MathSciNetMATHGoogle Scholar
  8. (8).
    D. Apsel:Int. J. Theor. Phys.,17, 643 (1978);Gen. Rel. Grav.,10, 297 (1979).MathSciNetCrossRefGoogle Scholar
  9. (9).
    Y. Takano:Lett. Nuovo Cimento,10, 747 (1974);Proceedings of the International Symposium on Relativity and Unified Field Theory (Calcutta, 1975–76), p. 17.MathSciNetCrossRefGoogle Scholar
  10. (10).
    The relationsR ij=Y iμYjλSμλ+2gij andR=S+6 have been used.Google Scholar
  11. (11).
    R. Fabbri:Nuovo Cimento B,56, 125 (1980).MathSciNetADSCrossRefGoogle Scholar
  12. (12).
    G. S. Asanov:Nuovo Cimento B,49, 221 (1979).MathSciNetADSCrossRefGoogle Scholar
  13. (13).
    M. Matsumoto:Tensor,34, 141 (1980).MathSciNetMATHGoogle Scholar
  14. (14).
    For example, ifC μλκ=C μ C λ C κ/C 2 (C 2=C μ C μ), thenS νμλκ=0. SeeM. Matsumoto andS. Numata:Tensor,34, 218 (1980).MathSciNetMATHGoogle Scholar
  15. (15).
    M. Matsumoto:Tensor,22, 201 (1971);L. Tamássy andM. Matsumoto:Tensor,33, 380 (1979).MathSciNetMATHGoogle Scholar
  16. (16).
    C. Brans andR. H. Dicke:Phys. Rev.,124, 925 (1961).MathSciNetADSCrossRefMATHGoogle Scholar
  17. (17).
    J. Cohn:Gen. Rel. Grav.,6, 143 (1975).ADSCrossRefGoogle Scholar
  18. (18).
    This kind of thing has often been considered in connection with Dirac’s conformally invariant theory.P. A. M. Dirac:Proc. R. Soc. London Ser. A,333, 403 (1973);D. Gregorash andG. Papini:Nuovo Cimento B,55, 37 (1980).MathSciNetADSCrossRefGoogle Scholar
  19. (19).
    F. Hehl, P. van der Heyde, G. Kerlick andJ. Nester:Rev. Mod. Phys.,48, 393 (1976);K. Hayashi andT. Shirafuji:Phys. Rev. D,19, 3524 (1979).ADSCrossRefGoogle Scholar
  20. (20).
    G. L. Murphy:Prog. Theor. Phys.,58, 1622 (1977);M. Gürses andM. Halil:Lett. Nuovo Cimento,27, 562 (1980).ADSCrossRefGoogle Scholar
  21. (21).
    K. Yano andE. T. Davies:Rend. Circ. Mat. Palermo,12, 211 (1963).MathSciNetCrossRefMATHGoogle Scholar
  22. (22).
    Heskia’s space is also regarded as a tangent space or a local Minkowski space withF μ λ κ(x)=0.S. Heskia:Prog. Theor. Phys.,45, 277, 640 (1971).ADSCrossRefGoogle Scholar
  23. (23).
    In the author’s theory of microgravitational field,y is regarded as the spacetime fluctuation and the transformation processR 8F 4 is slightly taken into account.S. Ikeda:Lett. Nuovo Cimento,25, 21 (1979).CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1981

Authors and Affiliations

  • S. Ikeda
    • 1
  1. 1.Department of Mechanical Engineering, Faculty of Science and TechnologyScience University of TokyoChibaJapan

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