# Gauge fields with vanishing scalar invariants

## TL;DR

This paper extends tensor analysis techniques to non-Abelian gauge fields, focusing on those with vanishing scalar invariants and universal Yang-Mills fields, revealing their unique properties and higher-order correction behaviors.

## Contribution

It introduces methods for analyzing gauge fields with special invariants and explores their implications for universal Yang-Mills solutions.

## Key findings

- Gauge fields with vanishing scalar invariants identified.
- Higher-order corrections to Yang-Mills equations vanish for these fields.
- New techniques for studying non-Abelian gauge covariant fields developed.

## Abstract

We consider extension of some established techniques of study of tensor fields on Lorentzian manifolds of arbitrary dimension to non-Abelian gauge covariant fields. These are then applied to study of gauge fields with vanishing scalar curvature invariants and universal Yang-Mills fields, for which all possible higher-order corrections to the Yang-Mills equation identically vanish.