Aspects of the quantization of non-linear electrodynamics in an uniform magnetic background
Abstract
The canonical and path integral quantization for non-linear electrodynamics in the presence of an external electromagnetic (EM) field are proposed in this work. The EM background field is introduced expanding a general lagrangian of a generic non-linear electrodynamics around the background for small fluctuations of the propagating fields, where we consider up to the quadratic terms in the propagating fields. As consequence, we obtain an electrodynamics linearized by the presence of the external EM field. Thereby, we study the canonical quantization calculating the energy for the ground state of the linearized EM field in terms of an external magnetic field. The microcausality of the model also is discussed through the Pauli-Jordan function. We also define a generating functional for the linearized EM field, in which, in the Coulomb gauge, the Green function of the model is obtained, and we can construct the perturbative formalism like in standard quantum field theory (QFT). As application of the perturbation theory, the effective potential at one loop is calculated for the linearized EM field coupled to a complex scalar field. We apply the results in the case of the Modified Maxwell ED.
Versions
Related
- Axion Electrodynamics in Presence of a Stellar Non-homogeneous Background Magnetic Field
- Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting
- Magnetic graphs for cavity quantum electrodynamics
- Long-range magnetic interaction within quantum electrodynamics formalism
- Static Magnetic Brane Solutions in Quartic Quasi-Topological Gravity with Power-Law Maxwell Nonlinear Electrodynamics
BibTeX
@misc{neves2026aspects,
title = {{Aspects of the quantization of non-linear electrodynamics in an uniform magnetic background}},
author = {M. J. Neves},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.00758},
eprint = {2608.00758},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00758},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Aspects of the quantization of non-linear electrodynamics in an uniform magnetic background
AU - M. J. Neves
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2608.00758
UR - https://arxiv.org/abs/2608.00758
AB - The canonical and path integral quantization for non-linear electrodynamics in the presence of an external electromagnetic (EM) field are proposed in this work. The EM background field is introduced expanding a general lagrangian of a generic non-linear electrodynamics around the background for small fluctuations of the propagating fields, where we consider up to the quadratic terms in the propagating fields. As consequence, we obtain an electrodynamics linearized by the presence of the external EM field. Thereby, we study the canonical quantization calculating the energy for the ground state of the linearized EM field in terms of an external magnetic field. The microcausality of the model also is discussed through the Pauli-Jordan function. We also define a generating functional for the linearized EM field, in which, in the Coulomb gauge, the Green function of the model is obtained, and we can construct the perturbative formalism like in standard quantum field theory (QFT). As application of the perturbation theory, the effective potential at one loop is calculated for the linearized EM field coupled to a complex scalar field. We apply the results in the case of the Modified Maxwell ED.
ER -