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

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.