  We give a Lagrangian description of an electric charge in a field sourced by
a continuous magnetic monopole distribution. The description is made possible
thanks to a doubling of the configuration space. The Legendre transform of the
nonrelativistic Lagrangian agrees with the Hamiltonian description given
recently by Kupriyanov and Szabo. The covariant relativistic version of the
Lagrangian is shown to introduce a new gauge symmetry, in addition to standard
reparametrizations. The generalization of the system to open strings coupled to
a magnetic monopole distribution is also given, as well as the generalization
to particles in a non-Abelian gauge field which does not satisfy Bianchi
identities in some region of the space-time.
