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.
Highlights
In non-Abelian gauge theories, a magnetic monopole may play an important role
To make A±μ massive, the VEV A+μ A−μ and caca was considered in Ref. [29]
First we show that the constant w in Eq(2.2) must be chosen as wA = φ0δA3 to preserve the BRS symmetry
Summary
In non-Abelian gauge theories, a magnetic monopole may play an important role. In the dual superconductor model of color confinement [1], monopole condensation is expected. Another way is to introduce a unit color vector nA(x) in the internal space [4, 5]. We briefly review ghost condensation and tachyonic gluon masses. 3, it is shown that these tachyonic masses are removed by the vacuum expectation value (VEV) A+μ A−μ. In the presence of the VEV A+μ A−μ , a magnetic potential is expected to become massive. We perform a singular gauge transformation, and derive the extended QCD with massive CμA. The tachyonic gluon mass is derived in the background covariant gauge in Appendix B. The BRS symmetry and the breakdown of the global gauge symmetry are explained in Appendix D
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