Proca tubes with the flux of the longitudinal chromoelectric field and the energy flux/momentum density

Abstract

We consider non-Abelian SU(3) Proca theory with a Higgs scalar field included. Cylindrically symmetric solutions describing classical tubes either with the flux of a longitudinal electric field or with the energy flux (and hence with nonzero momentum density) are obtained. It is shown that, in quantum Proca theory, there can exist tubes both with the flux of the longitudinal electric field and with the energy flux/momentum density simultaneously. An imaginary particle -- Proca proton~-- in which `quarks' are connected by tubes with nonzero momentum density is considered. It is shown that this results in the appearance of the angular momentum related to the presence of the non-Abelian electric and magnetic fields in the tube, and this angular momentum is a part of the Proca proton spin.