Classical electromagnetic field theory with quantum principal bundles

The aim of this paper is to formulate a non-commutative geometrical version of the classical electromagnetic field theory in the vacuum with the Moyal–Weyl algebra as the spacetime 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 Sec. [4], we present a mathematical model for which there are instantons that are not solutions of the corresponding Yang–Mills equation.