Zero modes of Gauss' constraint in gaugeless reduction of Yang - Mills theory

The physical variables for pure Yang - Mills theory in four - dimensional Minkowskian space time are constructed without using a gauge - fixing condition by the explicit resolving of the non - Abelian Gauss constraint. Gauge invariant variables are obtained by the use of the Bogoliubov transformation that diagonalizes the kinetic term in reduced action (action on constraint shell). As a result, the reduced action apart from a gauge invariant field variables depends on an additional global (only time - dependent) variable, describing zero mode dynamics of the Gauss constraint. >From the point of view of the gauge fixing method the additional variable gives the characteristic of the Gribov ambiguity: it is a collective variable corresponding to the group of transformation remaining after imposing the gauge condition. The perturbation theory in terms of quasiparticles with the new stable vacuum, which is defined through the zero mode configuration, is proposed. The Green functions for quasiparticles are determined after the averaging over the collective variable. It is conjectured that the degeneracy of quasiparticles states with respect to zero mode of constraint can be cause of the color confinement. (orig.)