We propose a unified extension of Maxwell’s equations that bridges axion electrodynamics with higher-dimensional geometric constraints, offering a singular theoretical framework to probe sub-atomic spacetime structures across both ultra-high-energy particle colliders and low-energy precision quantum-optical facilities. By integrating the topological $\theta$-term of pseudo-scalar axion fields with a hidden "soul" current $J_s$—derived from a $(4 + k)$-dimensional bulk Higgs–photon coupling—we formulate a generalized electrodynamic continuity law of the form:
$$d(*F - \theta F - J_s) = 0$$
In ordinary low-energy four-dimensional spacetime ($k = 0$), the extra-dimensional current vanishes identically ($J_s = 0$), smoothly recovering standard axion electrodynamics and classical Maxwellian behavior at macroscopic scales. At ultra-small distance scales ($\Delta x$) approaching the extra-dimensional compactification boundary $\Lambda$, however, the geometric interplay between axion–photon oscillations and the conserved topological soul-charge $Q_{\text{soul}}$ becomes dynamically active, with deviations from classical electrodynamics scaling as $\Lambda^{-2k}$.
We demonstrate that this combined topological framework yields complementary experimental signatures across opposite energy frontiers. In the high-energy regime, future collider facilities such as the Future Circular Collider (FCC) at CERN can probe high momentum transfers ($\Delta p$) near $\Lambda$ to simultaneously search for dark-matter axion candidates and extra spatial dimensions via precision measurements of anomalous Higgs–photon vertices and electroweak gauge extensions.
Conversely, in the low-energy tabletop regime, the cohomology obstruction class $\omega(\eta)$ encoded by $J_s$ induces a measurable degradation in quantum photon interference visibility, $1 - \mathcal{V} \sim \|\omega(\eta)\|^2 \Lambda^{-2k}$, alongside modified photon–axion conversion rates in intense magnetic fields. Furthermore, slowing and trapping light pulses inside ultra-cold atomic Bose–Einstein condensates (BEC) via electromagnetically induced transparency (EIT) provides a coherent light–matter storage medium capable of amplifying interaction times and imprinting topological phase and spin excitations without information loss.
| Experimental Regime | Physical Mechanism | Primary Observable |
|---|---|---|
| High-Energy Colliders (CERN/FCC) | High-$\Delta p$ probing near compactification scale $\Lambda$ | Anomalous $H\gamma$ vertex & axion production |
| High-Field Optical Interferometry | Cohomology obstruction $\omega(\eta)$ & $\theta F$ | Visibility loss $1 - \mathcal{V} \sim \|\omega(\eta)\|^2 \Lambda^{-2k}$ |
| Ultra-Cold Atomic BEC + EIT | Slow/stopped light spin-wave storage medium | Phase-coherent light–matter spin imprints |
@article{DeCeuster2026AxionHiggsContinuity,
author = {Peter De Ceuster},
title = {Topological Unification of Axion Electrodynamics and Higher-Dimensional Photon--Higgs Continuity},
journal = {Sig Labs Theoretical Physics & Quantum Electrodynamics Series},
year = {2026},
month = {November},
day = {7},
url = {https://peterdeceuster.uk/pen/axion},
note = {Published on peterdeceuster.uk/pen/axion}
}