Decomposing the Yang-Mills Field

TL;DR

The paper introduces an off-shell decomposition method for SU(N) Yang-Mills fields using Darboux theorem and gauge fixing, extending previous variable sets to a more general framework.

Contribution

It generalizes the Yang-Mills variable set to an off-shell framework via a novel decomposition based on Darboux theorem and coset space geometry.

Findings

Provides an off-shell gauge fixed decomposition of Yang-Mills connection.

Connects the decomposition to holomorphic and antiholomorphic forms on coset space.

Contains the original variables within the new off-shell framework.

Abstract

Recently we have proposed a set of variables for describing the physical parameters of SU(N) Yang--Mills field. Here we propose an off-shell generalization of our Ansatz. For this we envoke the Darboux theorem to decompose arbitrary one-form with respect to some basis of one-forms. After a partial gauge fixing we identify these forms with the preimages of holomorphic and antiholomorphic forms on the coset space $ SU(N)/U(1)^{N-1}$, identified as a particular coadjoint orbit. This yields an off-shell gauge fixed decomposition of the Yang-Mills connection that contains our original variables in a natural fashion.