= Solution
{c}
<Goldstone's theorem> states that in a relativistic <quantum field theory>, spontaneous breaking of an exact continuous global internal <symmetry> produces a massless <Goldstone boson> for each independent broken generator. More precisely, a conserved global current whose charge acts nontrivially on the <vacuum expectation value> has a massless pole in an appropriate current-field <correlation function>. The usual counting assumes a <Lorentz invariant> <vacuum state> and the standard locality and positivity hypotheses.
A local <gauge symmetry> is a <gauge redundancy>, so it does not by itself imply massless physical <Goldstone bosons>. In the <Higgs mechanism>, the corresponding scalar directions provide the longitudinal <polarizations> of massive <gauge bosons>.
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