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On Maxwell’s equations with a magnetic monopole on manifolds. (English. Russian original) Zbl 1433.53104
Proc. Steklov Inst. Math. 306, 43-46 (2019); translation from Tr. Mat. Inst. Steklova 306, 52-55 (2019).
Summary: 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 \(H^2(M)\) and \(H^3(M)\) are trivial, then solving these equations reduces to solving the d’Alembert-Hodge equation.
53C80 Applications of global differential geometry to the sciences
83C22 Einstein-Maxwell equations
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
Full Text: DOI
[1] Darboux, G., Problème de mécaniqie, Bull. Sci. Math. Astron., Sér. 2, 2, 1, 433-436 (1878)
[2] Poincaré, H., Remarques sur une expérience de M. Birkeland, C. R. Acad. Sci., 123, 530-533 (1896)
[3] Dirac, P. A M., Quantised singularities in the electromagnetic field, Proc. R. Soc. London A, 133, 60-72 (1931) · Zbl 0002.30502
[4] Mcdonald, K. T., Birkeland, Darboux and Poincaré: Motion of an electric charge in the field of a magnetic pole, E-print (2015), Princeton, NJ: Princeton Univ., Princeton, NJ
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