Mass Gap in Nonperturbative Quantization à La Heisenberg

Abstract

The approximate method of solving nonperturbative Dyson-Schwinger equations by cutting off this infinite set of equations to three equations is considered. The gauge noninvariant decomposition of SU(3) degrees of freedom into SU(2) × U(1) and SU(3)/(SU(2) × U(1)) degrees of freedom is used. SU(2) × U(1) degrees of freedom have nonzero quantum average, and SU(3)/(SU(2) × U(1)) have zero quantum average. To close these equations, some approximations are employed. Regular spherically symmetric finite energy solutions of these equations are obtained. Energy spectrum of these solutions is studied. The presence of a mass gap is shown. The obtained solutions describe quasi-particles in a quark-gluon plasma.