https://doi.org/10.1140/epjp/s13360-022-03066-y
Regular Article
Self-energy problem, vacuum polarization, and dual symmetry in Born–Infeld-type U(1) gauge theories
1
Department of Physics and Biruni Observatory, College of Sciences, Shiraz University, 71454, Shiraz, Iran
2
Department of Physics, Campus of Bijar, University of Kurdistan, Bijar, Iran
3
Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran
Received:
8
June
2022
Accepted:
11
July
2022
Published online:
25
July
2022
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 BI theory is the only theory with dual symmetry property (electric–magnetic duality) which reduces to the effective EH theory in the weak-field limit. The dual symmetry is broken when we demand an exact one-to-one correspondence in the weak-field limit with QED due to the vacuum polarization effects.
The original online version of this article was revised to deleted the second affiliation of the first author.
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-022-03281-7.
Copyright comment corrected publication 2022
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. corrected publication 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
