Ashtekar's Variables for Arbitrary Gauge Group

TL;DR

This paper generalizes Ashtekar's variables to arbitrary gauge groups with dimension at least three, providing a covariant gauge theory formulation that reduces to the known gravity formulation for SO(3,C).

Contribution

It introduces a new covariant gauge theory framework for arbitrary gauge groups, extending Ashtekar's variables beyond SO(3,C).

Findings

The theory is generally covariant for any gauge group of dimension ≥ 3.

The canonical form contains only first class constraints.

Reduces to Ashtekar's formulation for SO(3,C).

Abstract

A generally covariant gauge theory for an arbitrary gauge group with dimension $\geq 3$, that reduces to Ashtekar's canonical formulation of gravity for SO(3,C), is presented. The canonical form of the theory is shown to contain only first class constraints.