The Maxwell--Born--Infeld Theory: Presence of Finite-Energy Electric Point Charge and Absence of Monopole and Dyon

Abstract: We formulate a nonlinear electrodynamic theory which may be viewed as a weighted theory minimally interpolating the classical Maxwell and Born--Infeld theories. We show that, in contrast to the Born--Infeld theory, this new theory accommodates a finite-energy electric point charge, like that in the Born--Infeld theory, but does not accommodate a finite-energy magnetic point charge, known as the monopole, thereby exhibiting an electromagnetic asymmetry property, unlike that in the Born--Infeld theory. We estimate the radius of the electron within the formalism of such a theory. We also show that an electric point charge carries a finite energy in the Maxwell theory limit. Furthermore, we demonstrate that the theory does not accommodate a finite-energy monopole nor a dyon either in its most general setting.