Derivation of Maxwell’s Equations via the Feynman–Dyson Proof and Its Relativistic Generalization - Manuel Cabrera, Jaime; Arias Jiménez, Sergio Alberto; Lopez Arellano, Carlos Manuel; Paulin Fuentes, Jorge Mauricio (JOURNAL OF BASIC SCIENCES, 2025)
This work offers a detailed and conceptually transparent reconstruction of Feynman’s derivation of Maxwell’s equations, based on Newton’s second law and the use of Poisson brackets between coordinates and velocities in Euclidean space. While pedagogically motivated, our approach is technically rigorous and clarifies the foundational assumptions underlying both the original and relativistic versions of the derivation. We begin by revisiting the Lorentz force law in a classical Euclidean framework and then reformulate it covariantly using Minkowskian tensor calculus, incorporating the minimal coupling prescription as formally established by Montesinos and Perez-Lorenzana. Their contribution highlights how Feynman’s proof can be reconciled with a general and systematic application of the minimal coupling principle.