Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

==== What’s conservative (good): ====
* The derivation above is standard field theory: minimal coupling, Noether current, Maxwell’s equations → continuity equation. That’s a mathematically consistent backbone for QAT to stand on.
* Keeping h/2πh/2\pih/2π explicit is a choice of normalization and does not break the formal structure.

What remains model-dependent (needs care):
* Claiming the sphere surface is fundamental (as opposed to the usual volumetric field) requires specifying how strongly fields are localized to spherical shells. That manifests as boundary/surface terms or as constrained modes (spherical harmonics) in the quantum expansion.
* If you add surface-only coupling you must check self-consistency (matching surface boundary conditions to Maxwell equations in the volume, ensuring gauge invariance remains intact).

Testable ideas to pursue next:
# Surface-localized coupling: derive modified scattering amplitudes or cross sections for photon-electron interactions if the interaction is dominantly on a thin spherical shell — compare to QED predictions.
# Mode structure: quantize the coupled (ϕ,Aμ)(\phi, A_\mu)(ϕ,Aμ) system on a sphere and check whether energy levels/frequencies show any small shifts compared to standard atomic theory — predict a tiny spectral line shift as signature.
# Macroscopic signatures: if plasma or stellar-scale charge is distributed on large shells, this might influence polarization patterns or EM wave propagation in ways measurable by radio astronomy (careful astrophysical modeling required).