Non-Hermitian Schwinger effect in an imaginary magnetic field
Abstract
We investigate a non-Hermitian Schwinger effect by analyzing a one-loop effective Lagrangian of scalar and Dirac quantum electrodynamics (QED) in the presence of a real electric field and a parallel imaginary magnetic field. We show that an imaginary magnetic field produces an additional pole family in the integrand of the proper-time representation. Unlike a real magnetic field, an imaginary magnetic field can generate a nonzero imaginary part of the effective Lagrangian even in the absence of an electric field. The interplay between the two fields leads to nontrivial phenomena, such as a cancellation mechanism between the contributions of two fields. We also point out that when the ratio of two field strengths is rational, some poles among the two families coincide, and a careful treatment of double poles is required. By further examining the complex Landau-level structure of the electric-pole contribution, we find that the field dependence of the vacuum decay rate from each Landau level exhibits a sinusoidal-like behavior, and their sum determines the overall field dependence. Our results clarify the analytic structure of the QED effective Lagrangian in imaginary magnetic backgrounds and provide a basis for investigating its relation to non-Hermitian phenomena in the QED vacuum.
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BibTeX
@misc{arifi2026nonhermitian,
title = {{Non-Hermitian Schwinger effect in an imaginary magnetic field}},
author = {Ahmad Jafar Arifi and Kei Suzuki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36080},
eprint = {2610.36080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36080},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Hermitian Schwinger effect in an imaginary magnetic field
AU - Ahmad Jafar Arifi
AU - Kei Suzuki
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36080
UR - https://arxiv.org/abs/2610.36080
AB - We investigate a non-Hermitian Schwinger effect by analyzing a one-loop effective Lagrangian of scalar and Dirac quantum electrodynamics (QED) in the presence of a real electric field and a parallel imaginary magnetic field. We show that an imaginary magnetic field produces an additional pole family in the integrand of the proper-time representation. Unlike a real magnetic field, an imaginary magnetic field can generate a nonzero imaginary part of the effective Lagrangian even in the absence of an electric field. The interplay between the two fields leads to nontrivial phenomena, such as a cancellation mechanism between the contributions of two fields. We also point out that when the ratio of two field strengths is rational, some poles among the two families coincide, and a careful treatment of double poles is required. By further examining the complex Landau-level structure of the electric-pole contribution, we find that the field dependence of the vacuum decay rate from each Landau level exhibits a sinusoidal-like behavior, and their sum determines the overall field dependence. Our results clarify the analytic structure of the QED effective Lagrangian in imaginary magnetic backgrounds and provide a basis for investigating its relation to non-Hermitian phenomena in the QED vacuum.
ER -