Four-Four Maxwell Equations

Abstract: Electromagnetism is the energy originating from an electric charge. Our purpose is to enlarge Maxwell. Include the charge transfer phenomenology. A four bosons electromagnetism is derived. An EM completeness is achieved. The charge's set ${+,0,-}$ is intermediated by a quadruplet ${A_{\mu}, U_{\mu}, V^{\pm}_{\mu}}$. They are the usual photon $A_{\mu}$, massive photon $U_{\mu}$ and charged photons $V^{\pm}_{\mu}$. A new electric charge symmetry arises. It is ruled by an extended abelian symmetry $U_{q}\equiv U(1)\times SO(2)_{global}$. It generates a Lagrangian and three distinct Noether equations. An EM beyond charge-based emerges. Similarly, as mass is related to Newton laws, electric charge corresponds to the symmetry equation. Its associativity is more than being a coupling constant. It holds a field's flux. Maxwell is expanded. Amp`ere, Faraday, and Gauss laws are improved. Nonlinear granular and collective fields strengths were introduced. Potential fields are explicit. Polarization and magnetization vectors from first principles. New induced Faraday laws. Monopoles depend on fields. Spin-1 and spin-0 sectors separated covariants. The quadruplet completeness encodes a new EM energy. A journey from Maxwell to photonics is expressed. Seven EM integrated regimes are coursed. Maxwell, systemic, nonlinear, neutral, spintronics, electroweak, photonics. A new relationship for colliding light-light and light-matter appears. Selfinteracting photons are introduced.