Dirac and non-Dirac conditions in the two-potential theory of magnetic charge

Abstract

Abstract We investigate the Cabbibo–Ferrari, two-potential approach to magnetic charge coupled to two different complex scalar fields, $$\Phi _1$$ Φ1 and $$\Phi _2$$ Φ2 , each having different electric and magnetic charges. The scalar field, $$\Phi _1$$ Φ1 , is assumed to have a spontaneous symmetry breaking self-interaction potential which gives a mass to the “magnetic” gauge potential and “magnetic” photon, while the other “electric” gauge potential and “electric” photon remain massless. The magnetic photon is hidden until one reaches energies of the order of the magnetic photon rest mass. The second scalar field, $$\Phi _2$$ Φ2 , is required in order to make the theory non-trivial. With only one field one can always use a duality rotation to rotate away either the electric or magnetic charge, and thus decouple either the associated electric or magnetic photon. In analyzing this system of two scalar fields in the Cabbibo–Ferrari approach we perform several duality and gauge transformations, which require introducing non-Dirac conditions on the initial electric and magnetic charges. We also find that due to the symmetry breaking the usual Dirac condition is altered to include the mass of the magnetic photon. We discuss the implications of these various conditions on the charges.