Scalar-Longitudinal Modes of Extended Electrodynamics in Perfectly Conducting Waveguides and Divergence Cleaning Interpretation
Abstract
Extended electrodynamics keeps the scalar combination C=∇·A+μ0ε0∂Φ/∂ t as a dynamical field rather than imposing the Lorenz gauge condition, and this scalar adds a scalar-longitudinal (SL) family to the TE, TM and TEM modes. With C=0 on the wall of a closed perfectly conducting waveguide, the classical modes are unchanged. The SL modes have B=0 and an electric field along ∇ C, and their cutoffs are the Dirichlet eigenvalues of the cross-section, the same as the TM cutoffs, with no coaxial TEM counterpart. Charge-conserving sources with zero scalar data do not excite them. Matching at a conductor described by its constitutive laws gives ∂ C/∂ n=0 instead and couples the scalar-bearing modes to the Maxwell field. The results belong to the C=0 problem, the condition that separates the sectors and the one divergence cleaning uses, with benchmarks for the rectangular, circular cylinder, coaxial and L-shaped guides.
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BibTeX
@misc{rentzber2026scalarlongitudinal,
title = {{Scalar-Longitudinal Modes of Extended Electrodynamics in Perfectly Conducting Waveguides and Divergence Cleaning Interpretation}},
author = {Natan Rentzber and Jacob Howard and Fernando Minotti and Anatoliy Pinchuk and Giovanni Modanese},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28916},
eprint = {2610.28916},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28916},
}
RIS
TY - UNPB
TI - Scalar-Longitudinal Modes of Extended Electrodynamics in Perfectly Conducting Waveguides and Divergence Cleaning Interpretation
AU - Natan Rentzber
AU - Jacob Howard
AU - Fernando Minotti
AU - Anatoliy Pinchuk
AU - Giovanni Modanese
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28916
UR - https://arxiv.org/abs/2610.28916
AB - Extended electrodynamics keeps the scalar combination C=∇·A+μ_0ε_0∂Φ/∂ t as a dynamical field rather than imposing the Lorenz gauge condition, and this scalar adds a scalar-longitudinal (SL) family to the TE, TM and TEM modes. With C=0 on the wall of a closed perfectly conducting waveguide, the classical modes are unchanged. The SL modes have B=0 and an electric field along ∇ C, and their cutoffs are the Dirichlet eigenvalues of the cross-section, the same as the TM cutoffs, with no coaxial TEM counterpart. Charge-conserving sources with zero scalar data do not excite them. Matching at a conductor described by its constitutive laws gives ∂ C/∂ n=0 instead and couples the scalar-bearing modes to the Maxwell field. The results belong to the C=0 problem, the condition that separates the sectors and the one divergence cleaning uses, with benchmarks for the rectangular, circular cylinder, coaxial and L-shaped guides.
ER -