Confining boundary conditions from dynamical coupling constants for Abelian and non-Abelian symmetries

The present work represents among other things a generalization to the non-Abelian case of our previous result where the Abelian case was studied. In the U(1) case the coupling to the gauge field contains a term of the form g(Φ)jμ(Aμ + ∂μB), where B is an auxiliary field and jμ is the Dirac current. The scalar field Φdetermines the local value of the coupling of the gauge field to the Dirac particle. The consistency of the equations determines the condition ∂μΦjμ = 0 which implies that the Dirac current cannot have a component in the direction of the gradient of the scalar field. As a consequence, if ∂ has a soliton behavior, we obtain that jμ cannot have a flux through the wall of the bubble, defining a confinement mechanism where the fermions are kept inside those bags. In this paper, we present more models in Abelian case which produce constraint on the Dirac or scalar current and also spin. Furthermore a model that gives the MIT confinement condition for gauge fields is obtained. We generalize this procedure for the non-Abelian case and we find a constraint that can be used to build a bag model. In the non-Abelian case, the confining boundary conditions hold at a specific surface of a domain wall.