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We give a Lagrangian description of an electric charge in a field sourced bya continuous magnetic monopole distribution. The description is made possiblethanks to a doubling of the configuration space. The Legendre transform of thenonrelativistic Lagrangian agrees with the Hamiltonian description givenrecently by Kupriyanov and Szabo. The covariant relativistic version of theLagrangian is shown to introduce a new gauge symmetry, in addition to standardreparametrizations. The generalization of the system to open strings coupled toa magnetic monopole distribution is also given, as well as the generalizationto particles in a non-Abelian gauge field which does not satisfy Bianchiidentities in some region of the space-time.

Lagrangian formulation for electric charge in a magnetic monopole distribution