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 derive an off-shell generalization of this Ansatz. For this we envoke the Darboux theorem to decompose arbitrary one-form with respect to a natural 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, now identified as a particular coadjoint orbit. This yields an off-shell gauge fixed decomposition of the Yang-Mills field that contains our original variables in a natural fashion.