Magnetic monopoles in two time dimensions

Abstract

The observation of magnetic monopoles would lead to a symmetrization of Maxwell’s equations and provide explanations of fundamental properties such as the quantization of electric charge. Yet, in four dimensions, the covariant electromagnetic field tensor yields an action whose resulting field equations establish the absence of a magnetic charge. We here study the existence of magnetic monopoles in an extended space–time with a second time dimension, and construct the higher-dimensional gauge potential. This motivates the use of the Kalb–Ramond field, upon which a Kaluza–Klein-like reduction is performed under the assumption that the two time dimensions have no co-dependency. The resulting 5D electrodynamics contains a generalized version of Maxwell’s equations which contain magnetic charge densities whose source potential obeys a five-dimensional wave equation. As a second time dimension only acts on small length scales in the order of the Planck length, we provide a theory with symmetrized Maxwell’s equations including magnetic monopoles which do not violate current experimental evidence. We finally discuss the subsequent quantization of the electric charge as well as the weak interaction, equivalent to the violation of time reversal.