On Maxwell’s Equations with a Magnetic Monopole on Manifolds


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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.

About the authors

I. V. Volovich

Steklov Mathematical Institute of Russian Academy of Sciences

Author for correspondence.
Email: volovich@mi-ras.ru
Russian Federation, ul. Gubkina 8, Moscow, 119991

V. V. Kozlov

Steklov Mathematical Institute of Russian Academy of Sciences

Author for correspondence.
Email: kozlov@pran.ru
Russian Federation, ul. Gubkina 8, Moscow, 119991

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