Gauge Fields with Quasinilpotent Gauge Group

TL;DR

This paper explores a novel non-linear gauge theory based on the solvable Lie group HO(4,R), extending Maxwell's electromagnetism while maintaining gauge invariance, and highlights its unique mathematical properties and relation to standard Maxwell theory.

Contribution

It introduces a new Yang-Mills type gauge theory using the HO(4,R) group, a solvable Lie group with a nilpotent subgroup, expanding the class of gauge theories beyond traditional frameworks.

Findings

The theory maintains gauge invariance similar to Maxwell's electromagnetism.

The Yang-Mills equations for HO(4,R) are derived and analyzed.

Connections between the new theory and standard Maxwell theory are identified.

Abstract

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.