Hypothesis

Prompt

I have a theoretical physics hypothesis based on 3D Space (3+1 spacetime). The core premises are: Matter as Trapped Photons: Mass originates from self-confined, topological knots of electromagnetic waves (Toroidal Photon Model / Solitons). Charge as Symmetry Breaking: Charge is created when high-energy photon collisions break equilibrium into oppositely phase-tilted localized waves (\gamma + \gamma \to e^- + e^+). Antimatter as Phase Inversion: Antimatter corresponds to charge-conjugated phase inversion (\psi \to \psi^*) of the bound wave. Annihilation: Mass-to-energy conversion (E=mc^2) is the topological unknotting of the localized wave back into propagating photons. Act as a Theoretical Physicist specializing in Non-Linear Electrodynamics and Topological Field Theory. Help me formalize this idea using non-linear Maxwell equations and topological charge invariants (such as the Hopf Invariant). Provide a mathematical draft outlining the Lagrangian density for this model.