Abstract
An (n+1) factorization of an (n+1)-dimensional Riemann manifold is performed. For a space permitting a Killing vector, the (n+l)-dimensional Hubert variational principle reduces to the variational principle for the corresponding quantities in an n-dimensional space. Hence, setting n=4 and n=3, versions of a unified theory of gravitational, electromagnetic, and scalar fields and the steady-space theory of general relativity theory, respectively, are constructed. The five-dimensional variational principle for geodesics reduces to the four-dimensional leastaction principle for the test charged particle moving in gravitational, electromagnetic, and scalar fields.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
Y. M. Cho, J. Math. Phys.,16, 2029 (1975).
Y. M. Cho and P. S. Jang, Phys. Rev. D,12, 3789 (1975).
E. Cremmer and J. Scherk, Nucl. Phys.,B108, 409 (1976).
T. Kaluza, Sitzungber. Preuss. Acad. Wiss., 966 (1921).
P. G. Bergman, Introduction to Relativity Theory [in Russian], Nauka, Moscow (1947).
E. Schmutzer, Relativistische Physik, B. G. Teubner-Verlagsgesselschaft, Leipzig (1978).
Yu. S. Vladimirov and V. L Antonov, Vestn. Mosk. Gos. Univ., Fiz., Astron., No. 1 (1974).
Yu. G. Aliev, Yu. S. Vladimirov, and V. S. Nedopekin, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 8 (1974).
V. D. Gladush, Preprint ITF-78-64R, Kiev (1978).
A. L. Zel'manov, Dokl. Akad. Nauk SSSR,107, 815 (1956);209, 828 (1973);227, 78 (1976).
G. Denen, in: Einstein Collection 1969–1970 [in Russian], Nauka, Moscow (1970).
N. V. Mitskevich and V. N. Zakharov, Dokl. Akad. Nauk SSSR,195, 321 (1970).
R. F. Polishchuk, Dokl. Akad. Nauk SSSR,209, 1 (1973).
Yu. S. Vladimirov and V. I. Antonov, Preprint ITF-72-137R, Kiev (1972).
Yu. S. Vladimirov, Doctoral Dissertation, Minsk (1975).
L. D. Landau and E. M. Lifschitz, Field Theory [in Russian], Nauka, Moscow (1973).
N. A. Chernicov and E. A. Tagirov, Ann. Inst. Henri Poincaré,A9, No. 2, 109 (1968).
S. Kloster, M. M. Som, and A. Das, J. Math. Phys.,15, 1096 (1974).
L. D. Landau and E. M. Lifschitz, Mechanics [in Russian], Nauka, Moscow (1965).
A. A. Sokolov and D. D. Ivanenko, Quantum Field Theory [in Russian], GITTL, Moscow (1952).
D. Gromol, V. V. Klingenberg, and V. Meier, Riemann Geometry as a Whole [Russian translation], Mir, Moscow (1971).
S. Khokhing and J. Ellis, Large-Scale Structure of Space-Time [Russian translation], Mir, Moscow (1977).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 58–65, November, 1979.
Rights and permissions
About this article
Cite this article
Gladush, V.D. Five-dimensional theory of interacting scalar, electromagnetic, and gravitational fields. Soviet Physics Journal 22, 1172–1178 (1979). https://doi.org/10.1007/BF00894967
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00894967