Condensate $\langle A_μ^+A_μ^-\rangle$ and massive magnetic potential in Euclidean gauge theories

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.