Consistent gauge interaction involving dynamical coupling and anomalous current

Abstract

We show a possible way to construct a consistent formalism where the effective electric charge can change with space and time without destroying the gauge invariance. In the previous work[Formula: see text] we took the gauge coupling to be of the form [Formula: see text] where [Formula: see text] is an auxiliary field, [Formula: see text] is a scalar field and the current [Formula: see text] is the Dirac current. This term produces a constraint [Formula: see text] which can be related to MIT bag model by boundary condition. In this paper, we show that when we use the term [Formula: see text], instead of the auxiliary field [Formula: see text], there is a possibility to produce a theory with dynamical coupling constant, which does not produce any constraint or confinement. The coupling [Formula: see text] where [Formula: see text] is an anomalous current is also discussed.