BOSONIZATION OF QCD IN THE FIELD-STRENGTH APPROACH

The gluon sector of QCD is reformulated as an effective theory in a tensor field which is classically equivalent to the gluon field strength. Thereby the original Yukawa coupling of the quarks to the gluons is turned into an effective local four-quark interaction mediated by the inverse of the tensor field. The emerging effective quark theory is bosonized yielding an effective theory of colorless and colored "meson" fields, which is fully equivalent to the standard formulation of QCD in terms of quarks and gluons. For the gauge group SU(2) the effective meson action, which is implicitly defined by an integral over the tensor field, is explicitly evaluated in the semiclassical regime where the tensor field develops non-trivial vacuum configurations corresponding to the non-perturbative Yang-Mills vacuum. The effective meson action describes spontaneous breaking of chiral symmetry. This is shown by solving analytically the Schwinger-Dyson equation resulting from the stationary points of the effective meson action in the strong coupling limit and evaluating the quark condensates.