Nonlinear Conformal Electromagnetism

In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with only experimental need measure EL constants. modern language, their idea has been use Spencer sequence instead of Janet for Lie groupoid defining rigid motions space. Following H. Weyl, our purpose is compute first time conformal space-time in order provide mathematical foundations electromagnetism (EM), EM constant vacuum. With manifold dimension n, difficulty deal n transformations that have called “elations” by Cartan 1922. Using fact n=4 very specific properties computation cohomology, we prove there thus no conceptual difference between field or induction equations Maxwell equations. As byproduct, well known field/matter couplings (piezzoelectricity, photoelasticity, streaming birefringence, …) can be described abstractly, corresponding coupling The main consequence this paper revisit gauge theory (GT) because proved was depending on not U(1), shift one step left physical interpretation differential involved.