Abstract
A Maxwell space is a pair (M 4, F), where M 4 is a four-dimensional Minkowski space or a domain in it and F is a closed exterior differential 2-form on M 4. We describe classes of Maxwell spaces admitting translation groups of dimension 1–4.
Similar content being viewed by others
REFERENCES
H. Bacry, P. Combe, and P. Sorba, “Connected subgroups of the Poincare group, I,” Rep. Math. Phys., 5, No.2, 145–186 (1974).
H. Bacry, P. Combe, and P. Sorba, “Connected subgroups of the Poincare group, II,” Rep. Math. Phys., 5, No.3, 361–392 (1974).
O. G. Belova, A. N. Zarembo, M. A. Parinov, O. O. Sergeeva, and Yu. G. Ugarova, “Classification of static electromagnetic fields by subgroups of the Poincare groups,” Nauch. Tr. Ivan. Univ., Ser. Mat., 3, 11–22 (2000).
I. V. Bel’ko, “Subgroups of the Lorentz-Poincare group,” Izv. Akad. Nauk Belorus. SSR, Ser. Fiz.-Mat. Nauk, 1, 5–13 (1971).
A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin (1987).
P. Combe and P. Sorba, “Electromagnetic fields with symmetries,” Physica A, 80, No.3, 271–286 (1975).
B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry. Methods and Applications [in Russian], Nauka, Moscow (1979).
A. S. Ivanova and M. A. Parinov, “First integrals of Lorentz equations for some classes of electromagnetic fields,” Tr. Mat. Inst. Steklova, 236, 197–203 (2002).
A. Janner and E. Ascher, “Space-time symmetry of linearly polarized electromagnetic plane waves,” Lett. Nuovo Cim., 2, No.15, 703–705 (1969).
A. Janner and E. Ascher, “Space-time symmetry of transverse electromagnetic plane waves,” Helv. Phys. Acta, 43, No.3, 296–303 (1970).
A. Janner and E. Ascher, “Relativistic symmetry groups of uniform electromagnetic fields,” Physica A, 48, No.3, 425–446 (1970).
N. A. Kosheleva, A. K. Kuramshina, and M. A. Parinov, “Group classification of Maxwell spaces admitting elliptic helices,” Nauch. Tr. Ivan. Univ., Ser. Mat., 4, 73–82 (2001).
L. D. Landau and E. M. Lifshits, Field Theory [in Russian], Nauka, Moscow (1967).
D. A. L’vov and M. A. Parinov, “Group classification of Maxwell spaces admitting parabolic rotations,” Nauch. Tr. Ivan. Univ., Ser. Mat., 5, 51–62 (2002).
E. V. Morozova and M. A. Parinov, “Group classification of Maxwell spaces admitting translations along isotropic straight lines,” Nauch. Tr. Ivan. Univ,, Ser. Mat., 4, 87–94 (2001).
E. G. Morokhova, “Group classification of Maxwell spaces admitting proportional bi-rotations,” Nauch. Tr. Ivan. Univ., Ser. Mat., 5, 63–70 (2002).
M. A. Parinov, “Problem of group classification of electromagnetic fields,” in: Modern Methods of Function Theory and Related Topics [in Russian], Voronezh (1999), p. 156.
M. A. Parinov, “Group classification of Maxwell spaces,” in: Contemporary Analysis and Its Applications [in Russian], Voronezh (2000), p. 129–130.
A. I. Vorobiev, “Group classification of Maxwell spaces admitting hyperbolic helices,” Nauch. Tr. Ivan. Univ., Ser. Mat., 4, 35–42 (2001).
Author information
Authors and Affiliations
Additional information
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.
Rights and permissions
About this article
Cite this article
Parinov, M.A. Classes of Maxwell Spaces Admitting Translations. J Math Sci 129, 3642–3648 (2005). https://doi.org/10.1007/s10958-005-0303-z
Issue Date:
DOI: https://doi.org/10.1007/s10958-005-0303-z