Self-energy problem, vacuum polarization, and dual symmetry in Born-Infeld-type $U(1)$ gauge theories

TL;DR

This paper investigates Born-Infeld-type nonlinear electrodynamics, demonstrating finite self-energy for point charges in certain models, exploring vacuum polarization effects, and establishing connections with quantum electrodynamics (QED).

Contribution

It provides new proofs of finite self-energy in various BI-type theories and links classical BI models to QED predictions for vacuum polarization.

Findings

Finite self-energy for point charges in specific BI models.

Vacuum polarization effects in BI theories match QED predictions.

Weak-field limits of BI theories do not always regularize self-energy.

Abstract

We extensively explore three different aspects of Born-Infeld (BI) type nonlinear $U(1)$ gauge-invariant modifications of Maxwell's classical electrodynamics (also known as BI-type nonlinear electrodynamics) and bring some new perspectives on these theories. First, within the framework of exponential $U(1)$ gauge theory, it is explicitly proved that although the electric field at the location of the elementary point charges is not finite, but the total electrostatic field energy is finite. Motivated by this observation together with a wealth of evidence, we conjecture that all theories in 4-dimensional spacetime that belong to the BI family result in finite self-energy for elementary charged particles. In higher dimensions, it is found that the weak-field coupling limit of BI-type theories, which is identified as the weak field limit of effective Euler-Heisenberg (EH) theory, does not possess a regularizing ability to make the self-energy of a point charge finite, which implies that the conjecture may not hold for some BI-type theories. However, we explicitly prove that BI, logarithmic and exponential $U(1)$ gauge theories in arbitrary dimensions result in finite self-energy as well. Next, we classically study the problem of vacuum polarization effects and then systematically make a connection between all BI-type theories and QED. It is shown that all the BI-type theories classically predict the vacuum polarization effects, in which the final results are exactly in one-to-one correspondence with QED and the effective EH theory up to the leading order of corrections. Finally, we present a new, simple proof indicating that ...