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Particles and fields physics
We show that on three-dimensional Riemannian manifolds without boundaries and with trivial first real de Rham cohomology group (and in no other dimensions) scalar field theory and Maxwell theory are equivalent: the ratio of the partition functions is given by the Ray-Singer torsion of the manifold. On the level of interaction with external currents, the equivalence persists provided there is a fixed relation between the charges and the currents.
Prodanov, E., & Sen, S. (1999). Abelian Duality. Physical Reviews. D62, 045009. doi:10.1103/PhysRevD.62.045009.