Abstract
We consider a generalization of Maxwell’s equations on a pseudo-Riemannian manifold M of arbitrary dimension in the presence of electric and magnetic charges and prove that if the cohomology groups H2(M) and H3(M) are trivial, then solving these equations reduces to solving the d’Alembert—Hodge equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Darboux, “Problème de mécaniqie,” Bull. Sci. Math. Astron., Sér. 2, 2(1), 433–436 (1878).
H. Poincaré, “Remarques sur une expérience de M. Birkeland,” C. R. Acad. Sci. 123, 530–533 (1896).
P. A. M. Dirac, “Quantised singularities in the electromagnetic field,” Proc. R. Soc. London A 133, 60–72 (1931).
K. T. McDonald, “Birkeland, Darboux and Poincaré: Motion of an electric charge in the field of a magnetic pole,” E-print (Princeton Univ., Princeton, NJ, 2015), http://www.physics.princeton.edu/~mcdonald/examples/birkeland.pdf
Author information
Authors and Affiliations
Corresponding authors
Additional information
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Vol. 306, pp. 52–55.
Rights and permissions
About this article
Cite this article
Volovich, I.V., Kozlov, V.V. On Maxwell’s Equations with a Magnetic Monopole on Manifolds. Proc. Steklov Inst. Math. 306, 43–46 (2019). https://doi.org/10.1134/S0081543819050055
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543819050055