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In this paper we present a model which can produce boundary confiningcondition on Dirac field interacting with Abelian or non Abelian gauge fields.The constraint is generated by a scalar field. This kind of model can be thefoundation for bag models which can produce confinement. The present workrepresents among other things a generalization to the non Abelian case of ourprevious result where the Abelian case was studied. In the $U(1)$ case thecoupling to the gauge field contains a term of the form $g(\phi)j_\mu (A^{\mu}+\partial^{\mu}B)$ where $B$ is an auxiliary field and $j_\mu$ is the Diraccurrent. The scalar field $\phi$ determines the local value of the coupling ofthe gauge field to the Dirac particle. The consistency of the equationsdetermines the condition $\partial^{\mu}\phi j_\mu = 0$ which implies that theDirac current cannot have a component in the direction of the gradient of thescalar field. As a consequence, if $\phi$ has a soliton behavior, like defininga bubble that connects two vacuua, we obtain that the Dirac current cannot havea flux through the wall of the bubble, defining a confinement mechanism wherethe fermions are kept inside those bags. In this paper we present more modelsin Abelian case which produce constraint on the Dirac or scalar current andalso spin. Furthermore a model that give the M.I.T confinement condition forgauge fields is obtained. We generalize this procedure for the non Abelian caseand we find a constraint that can be used to build a bag model. In the nonAbelian case the confining boundary conditions hold at a specific surface of adomain wall.

Confining Boundary conditions from dynamical Coupling Constants for Abelian and non Abelian symmetries