- PII
- 10.31857/S0023476123700108-1
- DOI
- 10.31857/S0023476123700108
- Publication type
- Status
- Published
- Authors
- Volume/ Edition
- Volume 68 / Issue number 3
- Pages
- 401-406
- Abstract
- A geometric approach to describing an electromagnetic field in a medium with sources as a single field object is proposed. The description is based on the coordinate-free covariant approach adopted in the present-day geometrized field theories. Maxwell’s equations in a medium with sources are presented in terms of differential 2-forms for electric and magnetic fields in a four-dimensional space-time continuum. The general equations include special cases of propagation, scattering, and emission of an electromagnetic field in media with different properties.
- Keywords
- COORDINATE-FREE COVARIANT APPROACH FIELD THEORY
- Date of publication
- 15.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 13
References
- 1. Parrott S. Relativistic Electrodynamics and Differential Geometry. New York; Berlin; Heidelberg; London; Paris; Tokyo: Springer-Verlag, 1987. 308 p. https://doi.org/10.1007/978-1-4612-4684-8
- 2. Sattinger D.H. Maxwell’s Equations, Hodge Theory, and Gravitation. http://arxiv.org/abs/1305.6874v2. General Physics (physics.gen-ph) 3 Nov 2013. 22 p. https://doi.org/10.48550/arXiv.1305.6874
- 3. Schleifer N. // Am. J. Phys. 1983. V. 51. P. 1139. https://doi.org/10.1119/1.13325
- 4. Lindell I.V. Differential Forms in Electromagnetics. John Wiley & Sons. IEEE Press Series on Electromagnetic Wave Theory, 2004. V. 22. 272 p. https://doi.org/10.1002/0471723096.ch3
- 5. Warnick K.F., Russer P. // Prog. Electromagn. Res. 2014. V. 148. P. 83. https://doi.org/10.2528/PIER14063009
- 6. Дубровин Б.А., Новиков С.П., Фоменко А.Т. Современная геометрия. М.: Наука, 1986. 760 с.
- 7. Катанаев М.Н. Геометрические методы в математической физике. arXiv:1311.0733v3 [math-ph] 20 Nov 2016. 1588 с.
- 8. Ахиезер А.И., Берестецкий Б.Б. Квантовая электродинамика. М.: Наука, 1981. 428 с.
- 9. Федоров Ф.И. Оптика анизотропных сред. М.: Едиториал УРСС, 2004. 384 с.
