Electromagnetic Theory with Quantum Principal Bundles
arXiv:2309.11583 · doi:10.1142/S0129055X2550028X
Abstract
The aim of this paper is to formulate a {\it non--commutative geometrical} version of the classical electromagnetic field theory in the vacuum with the Moyal--Weyl algebra as the space--time by using the theory of quantum principal bundles and quantum principal connections. As a result we will present the correct Maxwell equations in the vacuum of the model, in which we can appreciate the existence of electric and magnetic charges and currents. Finally, in the fourth section we are going to present a {\it mathematical model} for which there are instantons that are not solutions of the corresponding Yang--Mills equation.