Emergence of the Photon from a Closed Quartic Variational Functional

A closed quartic variational functional is shown to generate a non-local propagating mode with zero effective mass, identified as the photon. Starting from the stationary condition, the Hessian structure is derived explicitly and exhibits a rigid Z3 cyclic closure with fixed spectral ratio L = 0.25. The non-local operator induced by the functional generates propagation with linear dispersion, while the internal cyclic structure reduces the physical degrees of freedom to a two-dimensional transverse subspace, yielding polarization and spin one without gauge assumptions. Interaction with localized configurations emerges directly from the quartic term, producing a coupling of the form J · A and a dynamical response equivalent to the Lorentz force. Quantization follows from the global selection functional, leading to discrete excitation levels without canonical procedures. The photon is therefore identified as a necessary non-local mode of a closed variational structure, uniquely determined by spectral rigidity and global coherence.