3+1 formulation of light modes in nonlinear electrodynamics

Kim Chul Min; Kim Sang Pyo

doi:10.1063/5.0240870

Volume 10 Issue 3

May 2025

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Kim Chul Min, Kim Sang Pyo. 3+1 formulation of light modes in nonlinear electrodynamics[J]. Matter and Radiation at Extremes, 2025, 10(3): 037201. doi: 10.1063/5.0240870

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Kim Chul Min, Kim Sang Pyo. 3+1 formulation of light modes in nonlinear electrodynamics[J]. Matter and Radiation at Extremes, 2025, 10(3): 037201. doi: 10.1063/5.0240870

Kim Chul Min, Kim Sang Pyo. 3+1 formulation of light modes in nonlinear electrodynamics[J]. Matter and Radiation at Extremes, 2025, 10(3): 037201. doi: 10.1063/5.0240870

Citation:

Kim Chul Min, Kim Sang Pyo. 3+1 formulation of light modes in nonlinear electrodynamics[J]. Matter and Radiation at Extremes, 2025, 10(3): 037201. doi: 10.1063/5.0240870

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3+1 formulation of light modes in nonlinear electrodynamics

doi: 10.1063/5.0240870

Kim Chul Min^{1, 2, 3
,
,
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Kim Sang Pyo^{4, 5
,
,}

1.
Advanced Photonics Research Institute, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea
2.
Center for Relativistic Laser Science, Institute for Basic Science, Gwangju 61005, South Korea
3.
Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea
4.
Department of Physics, Kunsan National University, Gunsan 54150, South Korea
5.
Asia Pacific Center for Theoretical Physics, Pohang 37673, South Korea

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Author Bio:
Author to whom correspondence should be addressed: sangkim@kunsan.ac.kr
Corresponding author: a)Electronic mail: chulmin@gist.ac.kr
Received Date: 2024-09-27
Accepted Date: 2025-03-03

Available Online: 2025-11-28

Publish Date: 2025-05-01

Abstract

Abstract

We present a 3+1 formulation of the light modes in nonlinear electrodynamics described by Plebanski-type Lagrangians, which include post-Maxwellian, Born–Infeld, ModMax, and Heisenberg–Euler–Schwinger QED Lagrangians. In nonlinear electrodynamics, strong electromagnetic fields modify the vacuum such that it acquires optical properties. Such a field-modified vacuum can possess electric permittivity, magnetic permeability, and a magneto-electric response, inducing novel phenomena such as vacuum birefringence. By exploiting the mathematical structures of Plebanski-type Lagrangians, we establish a streamlined procedure and explicit formulas to determine light modes, i.e., refractive indices and polarization vectors for a given propagation direction. We also work out the light modes of the various Lagrangians for an arbitrarily strong magnetic field. The 3+1 formulation advanced in this paper has direct applications to the current vacuum birefringence research: terrestrial experiments using permanent magnets/ultra-intense lasers for the subcritical regime and astrophysical observation of X-rays from highly magnetized neutron stars for the near-critical and supercritical regimes.

The authors have no conflicts to disclose.
Conflict of Interest
Chul Min Kim: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Sang Pyo Kim: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).
Author Contributions
The data that support the findings of this study are available from the corresponding author upon reasonable request.

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References(70)

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