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We show a possible way to construct a consistent formalism where theeffective electric charge can change with space and time without destroying theinvariance. In the previous work [1][2] we took the gauge coupling to be of theform $g(\phi)j_\mu (A^{\mu} +\partial^{\mu}B)$ where $B$ is an auxiliary field,$ \phi $ is a scalar field and the current $j_\mu$ is the Dirac current. Thisterm produces a constraint $ (\partial_{\mu}\phi) j^{\mu}=0 $ which can berelated to M.I.T bag model by boundary condition. In this paper we show thatwhen we use the term $ g(\phi)j_{\mu}(A^{\mu} -\partial^{\mu}(\frac{1}{\square}\partial_{\rho}A^{\rho})) $, instead of theauxiliary field $ B $, there is a possibility to produce a theory withdynamical coupling constant, which does not produce any constraint orconfinement. The coupling $ j_{\mu}^{A}(A^{\mu} -\partial^{\mu}(\frac{1}{\square}\partial_{\rho}A^{\rho})) $ where $ j_{\mu}^{A}$ is an anomalous current also discussed.

Consistent gauge interaction involving dynamical coupling and anomalous current