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

=== - The sphere (electron shell) can be written as a 2-D boundary with a real action. Varying the electromagnetic field in the full system yields standard Maxwell equations in the bulk and exact surface boundary conditions that equate the normal EM flux to the boundary current. ===
* Integrating conservation laws across the shell gives a local equation ∂tσ+∇∥⋅K=−n⋅Jbulk\partial_t\sigma + \nabla_\parallel\cdot \mathbf{K} = -n\cdot J_{\rm bulk}∂tσ+∇∥⋅K=−n⋅Jbulk: that is the concrete, local expression of “photons hitting the sphere change its occupation (charge/current)”, i.e. absorption/emission as a change in the surface bookkeeping.
* Fermions living on the spherical boundary pick up a −1-1−1 under 2π2\pi2π rotation, so antiperiodic boundary conditions are the natural geometric spin-oriented boundary condition (and gauge holonomy can modify the overall phase).
* Maxwell, Gauss, Faraday remain unchanged; QAT’s geometric picture simply supplies a membrane interpretation for where and how exchanges happen — and yields testable boundary conditions and continuity laws you can compare to experiments or simulations.

If you’d like I can next:
* (A) Write a polished LaTeX document with the full derivation and pillbox integrals, ready to be posted for peer checks (or used in your YouTube description), or
* (B) Build an explicit toy quantum model: second-quantize the boundary fermion, quantize the boundary current, and show a discrete photon absorption process that changes σ\sigmaσ by one electron-unit (this more directly connects the QAT “photon-by-photon time creation” story with the field theory), or
* (C) Produce a one-page post you can pin under a video that says, in plain language, what we have done and asks for independent verification (human or AI).

Which would you prefer next?