Calculation of gluon contribution to the proton spin by using the non-perturbative quantization \`a la Heisenberg

Abstract

The contribution of crossed gluon fields in flux tubes connecting quarks to the proton spin is calculated. The calculations are performed following non-perturbative Heisenberg's quantization technique. In our approach a proton is considered as consisting of three quarks connected by three flux tubes. The flux tubes contain color longitudinal electric and transversal electric and magnetic fields. The transversal fields causes the appearance of the angular momentum density. The dimensionless relation between the angular momentum and the mass of the gluon fields is obtained. The contribution to proton spin from rotating quarks and flux tubes connecting quarks is estimated. Simple numerical relation between the proton mass, the speed of light and the proton radius, which is of the same order as the Planck constant, is discussed.