Gauge Symmetry of Magnetic and Electric Two-Potentials with Magnetic Monopoles

We generalize the U(1) gauge transformations of electrodynamics by means of an analytical extension of their parameter space and observe that this leads naturally to two gauge potentials, one electric, one magnetic, which permit the writing of local Lagrangians describing elementary particles with electric and magnetic charges. Gauge invariance requires a conformal transformation of the metric tensor. We apply this approach, which borrows from Utiyama’s methodology, to a model with a massless scalar field and a model with a massless spinor field. We observed that for spinor models non-symmetrized Lagrangians can enable the existence of magnetic monopoles, but this is not possible with symmetrized Lagrangian. Such restrictions do not occur for spinless fields, but the model does not allow spin-one fields interacting with monopoles.