Anticommutative Electric and Magnetic Charges, and the Monopole Question

Abstract

The monopole question is treated anew in the light of a recent, strictly covariant,extended formulation of fermion quantum field theory naturally including alsoa pseudoscalar variety of conserved charges. The essential novelty lies in theresulting quantum property of anticommutivity between scalar and pseudoscalarcharge varieties, which should in particular apply to electric and magnetic charges.As an immediate outcome, there should no longer be any (Dirac-like) quantizationcondition relating these charges and binding the magnetic elementary charge tohave a very great strength. A generalized Lagrangian approach to the monopoleproblem is made truly viable, leading to two independent local gauge couplingswhich are separately generated by the electric and magnetic elementary chargesand are not allowed to interfere. This would prevent electric and magneticmonopoles from mutually interacting and would particularly account for the“absence” of magnetic sources in ordinary electromagnetism. Within such aframework, an electric charge eigenstate with a nonzero eigenvalue is bound tohave a null magnetic charge expectation value, and the magnetic dipole momentof an electrically charged point fermion may actually be seen as resulting fromthe additional internal presence of a single magnetic charge subjected to a maximaluncertainty in sign. An easy estimate makes it allowable to assign to this chargea strength just equal to that of the partner electric charge. Such a conjecture leadsto a “dual” model of a charged point fermion where the “electric” and “magnetic”roles can well be interchanged with no observable effects. In the associatedformalism, duality symmetry is already included without the need to appeal toany “missing” electromagnetic phenomenology to be discovered.