Condensate $⟨A_{\mu }^{+}{A}_{\mu }^{-}⟩$ and massive magnetic potential in Euclidean gauge theories

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 $⟨A_{\mu }^{+}{A}_{\mu }^{-}⟩$. Because of the ghost condensation, monopole solutions are included naturally. We find that the condensate $⟨A_{\mu }^{+}{A}_{\mu }^{-}⟩$ makes the magnetic potential massive.