Decomposing the Yang-Mills Field

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 $SU(N)\mathrm{/}U(1{)}^{N-1}$, 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.