The definition of *gauge equivalence* and notations used here is the same as those in my previous question.

As we know, the condition $\chi_{ij}'=G_i\chi_{ij}G_j^\dagger$(where $G_i\in SU(2)$) is a *sufficient condition* for the $H$ and $H'$ being gauge equivalent, but is it also a *necessary condition*? If not, then what's the *necessary and sufficient condition* for gauge equivalence? Is my conjecture (1) correct?

Thanks in advance.

This post imported from StackExchange Physics at 2014-03-09 08:39 (UCT), posted by SE-user K-boy