Abstract
Nonlinear equations are derived for mass as well as massless vector fields in a Riemann space, where nonlinearity is induced by the interaction of these fields with individual irreducible parts of the torsion tensor. It is shown that in the simplest cases these equations are exactly solvable for an electromagnetic field, while a mass field is described by a number of interesting equations, in particular the sinh-Gordon equation, which has soliton solutions.
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V. N. Ponomarev and E. V. Smetanin, Vestn. Mosk. Univ., Ser. Fiz. Astron., No. 5, 29–37; No. 6, 3–8 (1978).
E. V. Smetanin, In: Abstracts of Contributed Papers for the Discussion Groups at the Ninth International Conference on General Relativity and Gravitation (F. Schiller, ed.), Jena (East Germany) (1980), pp. 649–650.
F. W. Hehl, P. von der Heyde, G. D. Kerlik, and J. M. Nester, Rev. Mod. Phys.,48, No. 3, 393–416 (1976).
V. De Sabbata and M. Gasperini, Phys. Lett. A,77, No. 5, 300–302 (1980).
S. Hojman, M. Rosenbaum, M. P. Ryan, and L. C. Shepley, Phys. Rev. D,17, No. 12, 3141–3146 (1978).
C. Mukku and W. A. Sayed, Phys. Lett. B,82, Nos. 3–4, 382–386 (1979).
V. I. Rodichev, Zh. Eksp. Teor. Fiz.,40, No. 5, 1469–1473 (1961).
V. G. Krechet and V. N. Ponomarev, Acta Phys. Pol. B,7, No. 8, 553–556 (1976).
D. Ivanenko, in: Quanta, Relativity, and Cosmology, Johnson Reprint Corp., New York (1976), pp. 295–354.
G. Mie, Ann. Phys. (Leipzig),37, No. 3, 511–534 (1912).
V. Yu. Urbakh, Dokl. Akad. Nauk SSSR,101. No. 6, 1043–1046 (1955).
D. Ivanenko and A. Sokolov, Classical Field Theory [in Russian], GITTL, Moscow-Leningrad (1949), pp. 194–206.
V. N. Ponomarev, Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys.,19, 545–550 (1971).
V. Yu. Urbakh, Zh. Eksp. Teor. Fiz.,35, No. 1, 208–215 (1958).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 28–32, January, 1982.
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Smetanin, E.V. The Maxwell and Proca equations in spaces with torsion. Soviet Physics Journal 25, 26–30 (1982). https://doi.org/10.1007/BF00893868
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DOI: https://doi.org/10.1007/BF00893868