Gauge Fields with Quasinilpotent Gauge Group

We investigate non-linear generalization of Maxwell theory of electromagnetic field keeping the gauge invariance of Lagrangian. New theory, which is standard Yang-Mills theory, is based on Harmonic Oscillator HO(4,R) gauge group. It’s a solvable Lie group with nilpotent normal subgroup of codimension 1. We write down the Yang-Mills equation and point out their pecularities and connection with standard Maxwell theory.