Four–Four Maxwell equations

Abstract

Electromagnetism is the energy originating from an electric charge. Our purpose is to enlarge Maxwell and include the charge transfer phenomenology. A four-boson electromagnetism is derived. An electromagnetic (EM) completeness is achieved. The charge’s set [Formula: see text] is intermediated by a quadruplet [Formula: see text]. They are the usual photon [Formula: see text], massive photon [Formula: see text] and charged photons [Formula: see text]. A new electric charge symmetry arises. It is ruled by an extended abelian symmetry [Formula: see text]. It generates a Lagrangian and three distinct Noether equations. An electromagnetism that goes beyond charge-based interactions 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. Ampère, Faraday, and Gauss laws are improved. An abelian nonlinear model is proposed. Nonlinear granular and collective fields strengths were introduced. Potential fields are explicit. Polarization and magnetization vectors are from first principles with new induced Faraday laws. Monopoles depend on fields. Spin-1 and spin-0 sectors are separated covariantly. Uncharged and charged gauge vector fields are unified. 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, and photonics. A new relationship for colliding light–light and light–matter appears. Self-interacting photons are introduced.