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A four-dimensional electrodynamic model of a free photon state is proposed, in which corpuscular and wave properties are considered as different manifestations of a single localized field configuration in a space with an additional physical coordinate $w$. The observable three-dimensional space corresponds to the hypersurface $w=0$, and the state dynamics is described by an extended four-dimensional Maxwell system. The model connects the kinematic, energetic, field, and geometrical characteristics of the photon state within a single structure. In particular, the observed propagation velocity, energy, momentum, internal dynamics along the additional direction, and spatial scales of the electromagnetic manifestation are considered as interrelated properties of a single bound four-dimensional mode. The characteristic transverse scale of the state is proportional to the observed wavelength, defining the geometrical structure of the localized field configuration. Within the model, the free photon state possesses a subluminal observed velocity $v_x<c$, and the corresponding Lorentz factor relates the observed kinematics to the energy of the kinematic component, the momentum orientation in the $(x,w)$ plane, and the internal dynamics of the state. In the regular relativistic regime, an asymptotic relation $\gamma\propto\omega$ emerges. The four-dimensional field system introduces hidden and mixed components connecting the observable electromagnetic sector with the dynamics along the additional coordinate. The total energy of the bound state is separated into kinematic and field contributions, while transitions between stable states are described as a joint reconstruction of the kinematic and field structures. The obtained results lead to several experimental directions, including the search for vacuum frequency-dependent propagation delay, testing of the characteristic spatial scale of the bound state, and investigation of a finite re-stabilization region after a local perturbation of a formed wave.
Kazakov V. V. 2026. Four-Dimensional Electrodynamics of a Bound Photon State. PREPRINTS.RU. https://doi.org/10.24108/preprints-3116537
