ar X iv : h ep - p h / 97 11 34 7 v 2 1 9 N ov 1 99 7 QCD 2 in the modified Fock – Schwinger gauge

The system of light quark and heavy antiquark source is studied in 1+1 QCD in the large N C limit. The situation is demonstrated to be the two dimensional analogue of the problem in 3+1 QCD corresponding to the essentially nonlocal case of zero vacuum correlation length, which does not allow perturbative treatment. The modified Fock–Schwinger gauge condition is employed to derive the effective Dirac-type equation for the spectrum, which is proved to be equivalent to the 't Hooft equation in the limit of one heavy mass. The chiral condensate is shown to appear naturally in the given approach and to coincide with the standard value. Theory of quarks in 1+1 dimensions interacting via gluons in the large N C limit has a long history. It was in 70-th when the celebrated 't Hooft equation for the meson spectrum in such a model was derived in the light-cone gauge (A − = 0) [1] and then re-derived in the axial gauge (A 1 = 0) [2]. Since that time it has done it credit to every new approach to the realistic 3+1 QCD to reproduce this equation when applied to a much more simple and physically clear 1+1 't Hooft model. Many theories have passed this examination with honour. Recently there was suggested a new approach to the theory of light spinning quarks in the confining vacuum [3], that allowed, in the large N C limit, to obtain a nonlinear Dirac-type equation for the light quark motion in the nontrivial vacuum of QCD in presence of heavy antiquark source. Despite of its nonlocality, this equation allows a systematic analysis, which was started in our previous work [5] and led to the conclusion that the two cases of small and large vacuum correlation length T g , value which defines the distances where vacuum gluonic fields are correlated, differ drastically, viz. for the case of large T g (T g ≫ 1 m , where m is the mass of the light quark) the nonlocality can be treated pertur-batively, whereas the opposite limiting case of small T g (T g ≪ 1 m) turned out sufficiently *