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

Tengyang Liu, Yisong Yang

TL;DR

The paper presents Maxwell–Born–Infeld (MBI) theory as a weighted interpolation between Maxwell and Born–Infeld electrodynamics, governed by $\mathcal{L}(\mathcal{F})=\kappa_1\mathcal{F}+\frac{\kappa_2}{\beta}(1-\sqrt{1-2\beta\mathcal{F}})$ with $\kappa_1+\kappa_2=1$. It proves that this framework admits a finite-energy electric point charge like BI but does not support a finite-energy magnetic monopole or dyon, establishing a robust electromagnetic asymmetry. The point-charge energy factors as $E/4\pi=(q^2/a)H(\kappa_1,\kappa_2)$ with $a=\beta^{1/4}q^{1/2}$, and the normalized energy $H$ decreases with $\kappa_2$, yielding a finite-energy Maxwell limit $H\to\frac{4}{3}$ as $\kappa_2\to0$ and a corresponding electron-radius ratio $r_{MBI}/r_e\to\frac{20}{9}$. The paper further analyzes general electrostatic settings, showing that radial, singly-centered charge distributions avoid magnetic currents, while asymmetric distributions induce magnetic currents, and provides bounds and Fatou-type results for energies. These findings have implications for nonlinear electrodynamics and point-charge modeling, with future work aimed at gravitational extensions and broader BI-generalizations.

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.

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

TL;DR

The paper presents Maxwell–Born–Infeld (MBI) theory as a weighted interpolation between Maxwell and Born–Infeld electrodynamics, governed by with . It proves that this framework admits a finite-energy electric point charge like BI but does not support a finite-energy magnetic monopole or dyon, establishing a robust electromagnetic asymmetry. The point-charge energy factors as with , and the normalized energy decreases with , yielding a finite-energy Maxwell limit as and a corresponding electron-radius ratio . The paper further analyzes general electrostatic settings, showing that radial, singly-centered charge distributions avoid magnetic currents, while asymmetric distributions induce magnetic currents, and provides bounds and Fatou-type results for energies. These findings have implications for nonlinear electrodynamics and point-charge modeling, with future work aimed at gravitational extensions and broader BI-generalizations.

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.

Paper Structure

This paper contains 6 sections, 1 theorem, 75 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. A new nonlinear electrodynamic theory
  3. An electric point charge
  4. Absence of finite-energy monopole and dyon across the theory
  5. Electrostatic solution in the general setting
  6. Conclusions

Key Result

Theorem 1

The static equations of motion of the theory always allow a unique solution describing a finite-energy electric point charge but never allow a solution giving rise to a finite-energy monopole or dyon. Furthermore, these equations can also be solved in the general situation where the electric charge where $H$ is a constant depending only on the weight parameters, which enables us to estimate the e

Figures (2)

  • Figure 1: The normalized energy $H(\kappa_1,\kappa_2)$ plotted over the full parameter range $0<\kappa_2\leq 1$.
  • Figure 2: The normalized energy $H(\kappa_1,\kappa_2)$ of an electric point charge in relation to its explicit lower bound $H_1(\kappa_1,\kappa_2)$ and upper bound $H_2(\kappa_1,\kappa_2)$ plotted over the weight parameter $\kappa_2$ showing the convergence of these quantities as $\kappa_2\to1$.

Theorems & Definitions (1)

  • Theorem 1