Zero Modes of Gauss' Constraint in Gaugeless Reduction of Yang - Mills Theory

Abstract

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 and by the Bogoliubov transformation that diagonalizes the kinetic term in reduced action (action on constraint shell). As a result, the reduced action is expressed in terms of gauge invariant field variables including an additional global (only time - dependent) one, describing zero mode dynamics of the Gauss constraint. This additional variable reflects the symmetry group of topologically nontrivial transformations remaining after the reduction. ( It gives also the characteristic of the Gribov ambiguity from the point of view of the gauge fixing method.) The perturbation theory in terms of quasiparticles with the new stable vacuum, which is defined through the zero mode configuration, is proposed. It is shown, that the averaging of Green's functions for quasiparticles over the global variable leads to the mechanism of color confinement.