Consistent gauge interaction involving dynamical coupling and anomalous current

TL;DR

This paper proposes a formalism for a gauge theory with a space-time varying electric charge, avoiding constraints and confinement, by using a specific gauge interaction term involving an anomalous current.

Contribution

It introduces a new approach to construct gauge theories with dynamical coupling constants without constraints, using a modified interaction term involving an anomalous current.

Findings

The formalism allows the electric charge to vary in space and time.

The approach avoids constraints and confinement issues present in previous models.

It extends the gauge interaction framework to include anomalous currents.

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 invariance. In the previous work [1][2] we took the gauge coupling to be of the form $g(\phi)j_\mu (A^{\mu} +\partial^{\mu}B)$ where $B$ is an auxiliary field, $ \phi $ is a scalar field and the current $j_\mu$ is the Dirac current. This term produces a constraint $ (\partial_{\mu}\phi) j^{\mu}=0 $ which can be related to M.I.T bag model by boundary condition. In this paper we show that when we use the term $ g(\phi)j_{\mu}(A^{\mu} - \partial^{\mu}(\frac{1}{\square}\partial_{\rho}A^{\rho})) $, instead of the auxiliary field $ B $, there is a possibility to produce a theory with dynamical coupling constant, which does not produce any constraint or confinement. 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.