= Solution
A symmetry generated by $Q^a$ is spontaneously broken when the vacuum is not invariant:
$$
Q^a|0\rangle\ne0.
$$
A local <order parameter> is obtained by finding a field $\varphi_m$ for which
$$
\boxed{\langle0|[Q^a,\varphi_m(0)]|0\rangle
=-(T^a)_{mn}\langle0|\varphi_n(0)|0\rangle\ne0},
$$
with the sign depending on the commutator convention. This criterion is useful in infinite volume because it can remain finite even when the spatially integrated charge itself is not a well-defined normalizable operator.
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