Dynamics of quarks and gauge fields in the lowest-energy states in QCD and QED

We examine the dynamics of quarks and gauge fields in QCD and QED interactions in the lowest energy states with approximate cylindrical symmetry, as in a flux tube. Using the action integral, we separating out the (3+1)D space-time in terms of the transverse and the longitudinal degrees of freedom and solve the resultant equations of motion. We find that there are localized and stable states of QCD and QED collective excitations, showing up as particles whose masses depend on the QCD and QED coupling constants and the flux-tube radius. Along with stable collective QCD excitations of the quark-QCD-QED system, there may be stable QED collective excitations at the lower energies of many tens of MeV.