Quark Confinement in Restricted SU(2) Gauge Theory

Abstract

We apply Zwanziger formalism to Cho restricted $ SU(2) $ theory to obtain the potential in a static quark-antiquark pair. Cho restricted theory is a self-consistent subset of a non-Abelian $ SU(2) $ gauge theory which tries to describe the infrared regime of Yang-Mills gauge theories. In Zwanziger formalism, a local Lagrangian depending on two electric and magnetic gauge fields is constructed for the theories where both electric and magnetic charges exist. Based on this local Lagrangian the propagator and then the potential between quarks is calculated in two limits: $ m_{C} r \ll 1 $ and $ m_{C} r \gg 1$, where $ m_{C} $ is the mass of the dual gauge boson and $ r $ is the distance between the quark and the antiquark.