In this physicsforums post (post #10), @samalkhaiat states that the Goldstone bosons can be parameterized by a matrix acting on the vacuum state (which in general can be represented by some vector, →v).
Explicitly the user claims that we can write,
ϕi=R(g(x))i,jvj
where g(x), if I understand correctly, are the group generators of the unbroken group. How come this is justified?