Glueball filled with the quark field as a model of nucleon

Abstract

On the basis of the non-perturbative Heisenberg's quantization scheme and using some simplifications and assumptions the reduction from the gluon-quark Lagrangian to a scalar-fermion Lagrangian is made. The corresponding field equations have a regular spherically symmetric solution which can be interpret as a simplified model of nucleon. Some properties of such "nucleon" are discused: the presence of a mass gap and spin $\neq \hbar /2$. The mass gap describes the difference between the "nucleon" and the "nucleon" without quark field (a scalar glueball). The presence of spin $\neq \hbar /2$ can be connected with the spin problem of nucleon.