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

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