Proca Electrodynamics Approach to The Massive Photon

The work presents a reflection on the importance of the existence of a massive photon. The discussion takes place based on the development of Maxwell's electrodynamics, introducing the massive term for the photon through Proca's electrodynamics. The presentation was based on theoretical development with the exposure of derivations by the divergent and rotational electromagnetic field, imposing the subsidiary condition with the terms of vector potentials. The work was intended to be simple, not going into details regarding applications and even Lagrangian terms, gauge transformations, and conservation of energy and momentum. The objective of this work is to discuss the possibility of the massive photon, through the derivation terms using divergent and rotational electromagnetic fields by extending the Proca model, presenting the dispersion relationship and consolidating with the Compton length and relating it to Planck's constant to understand the additional massive parameter of the theory. We made a comparison of some researchers in relation to experimental data, where they used an upper limit for the photon mass. We consolidate with a reflection on the study of the massive photon and its effects.