  The aim of this paper is to formulate a non--commutative geometrical version
of the Classical Electromagnetic Field Theory in the Moyal--Weyl algebra by
using the Theory of Quantum Principal Bundles and Quantum Principal
Connections. As a result, we will present the correct equations of motion of
two systems: an electromagnetic field in the vacuum and scalar matter and
antimatter coupled to an electromagnetic field. In particular, we prove the
existence of electric and magnetic charges and currents conserved in the
vacuum.
