A new look at the $SU_2$ gauge monopole

An $SU_2\times U_1$ scalar vector model with a scalar doublet $φ$ is reviewed for the study of possible magnetic monopole solution. An eigenvalue equation $\hat n^a σ^a φ_\pm =\pm φ_\pm$ is shown to induce a set of monopole solutions specified by the unit vector $\hat n$. It is shown clearly that monopole solution has to do with the eigenvalue equation and an unique covariant combination of the non-abelian gauge field. It is also shown that a new set of monopole solutions is presented as a generalization of the monopole solutions known as Cho-Maison monopole. We also show that the EM field and field tensor defined by CM solution is effectively the same as the effective covariant field tensor introduced in this paper. Possible implication is also discussed in the literature.