CHIRAL-SYMMETRY BREAKING IN THE DISORDERED QCD VACUUM

The spectrum of quark eigenvalues nu(LAMBDA) is found for an ensemble of vacuum fields, consisting of statistically independent pieces ("elementary fields"). The spectrum nu(LAMBDA) is the Wigner semicircle curve, centered around poles of the "elementary" S matrix. Spontaneous chiral-symmetry breaking occurs when overlap integrals of different pieces are larger than the displacement of these "elementary" poles from the zero point. For the instanton-gas model the corresponding spectrum density is exactly reproduced, and a discussion of numerical studies of the instanton liquid is given. A general mechanism of chiral-symmetry restoration is briefly outlined.