Condensate $\langle A_{\mu}^+A_{\mu}^-\rangle$ and massive magnetic potential in Euclidean gauge theories

TL;DR

This paper investigates how ghost condensation in Euclidean SU(2) gauge theory leads to a gauge field condensate that removes tachyonic masses and results in a massive magnetic potential, providing insights into nonperturbative phenomena.

Contribution

It demonstrates that the gauge field condensate $raket{A_{ u}^+A_{ u}^-}$ removes tachyonic masses and induces a massive magnetic potential in a nonlinear gauge setting.

Findings

Ghost condensation occurs in the nonlinear gauge.

Gauge field condensate removes tachyonic masses.

Magnetic potential becomes massive due to the condensate.

Abstract

Euclidean $SU(2)$ gauge theory is studied in a nonlinear gauge. In this theory, ghost condensation happens and gauge fields acquire tachyonic masses. It is shown that these tachyonic masses are removed by a gauge field condensate $\langle A_{\mu}^+A_{\mu}^-\rangle$. Because of the ghost condensation, monopole solutions are included naturally. We find the condensate $\langle A_{\mu}^+A_{\mu}^-\rangle$ makes the magnetic potential massive.