On the Decomposition Theorem for Gluons

Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about possibility to separate AM from in gauge invariant manner are based on ansatz that gluon field can be presented form decomposition where physical components additive pure components, i.e. Aμ = $$A_{\mu }^{{{\text{phys}}}}$$ + }^{{{\text{pure}}}}$$ . In present paper, we show non-Abelian theory this a strong mathematical evidence frame contour conception. other words, reformulate as theorem and, then, use prove theorem. first time, also demonstrate possesses special kind residual related boundary configurations expressed terms fields. As result, trivial conditions lead inference includes only provided by condition.