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 invariance. In the previous work [1][2] we took the gauge coupling to be of the form $g(\varphi )j_{\mu }(A^{\mu }+{\partial }^{\mu }B)$ where $B$ is an auxiliary field, $\varphi$ is a scalar field and the current $j_{\mu }$ is the Dirac current. This term produces a constraint $({\partial }_{\mu }\varphi )j^{\mu }=0$ which can be related to M.I.T bag model by boundary condition. In this paper we show that when we use the term $g(\varphi )j_{\mu }(A^{\mu }-{\partial }^{\mu }(\frac{1}{\square }{\partial }_{\rho }{A}^{\rho }))$, 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.

arXiv admin note: substantial text overlap with arXiv:1406.1316, arXiv:1311.2536

References in corpus (4)

• Local electromagnetic duality and gauge invariance
• Coupling Electromagnetism to Global Charge
• Confining Boundary conditions from dynamical Coupling Constants
• Confining Boundary conditions from dynamical Coupling Constants for Abelian and non Abelian symmetries