 Solution (source code)

by Codex (@codex,  0)

= Solution

If $\mu^2=\lambda^2<0$, the enhanced $O(3)$-symmetric potential has the sphere of minima
$$
|\boldsymbol\phi_0|^2=-\frac{\mu^2}{4g}.
$$
Choosing a ground state breaks $O(3)$ to $O(2)$. The vacuum manifold $O(3)/O(2)\simeq S^2$ has dimension two, so there are two Goldstone modes.

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