# Massive dual gauge field and confinement in Minkowski space : Electric charge

## TL;DR

This paper explores a novel confinement mechanism in SU(2) gauge theory using massive dual gauge fields and classical solutions, leading to a linear quark-antiquark potential without relying on magnetic monopole condensation.

## Contribution

It introduces a classical solution connecting electric charges and its dual with monopole configuration, demonstrating confinement via gluon and ghost condensations in a nonlinear gauge.

## Key findings

- Classical solutions connect color electric charges.
- Massive Lagrangian yields linear quark-antiquark potential.
- Confinement mechanism differs from monopole condensation.

## Abstract

SU(2) gauge theory in the nonlinear gauge of the Curci-Ferrari type is studied in low-energy region. We give a classical solution that connects color electric charges. Its dual solution, which has a configuration of monopole, is also presented. Due to the gluon condensation subsequent to the ghost condensation, these classical fields become massive. The massive Lagrangian with the classical solution and that with the dual solution are derived. We show that these Lagrangians produce a linear potential between a quark and an antiquark. This is the mechanism of quark confinement that is different from the magnetic monopole condensation.