I’m trying to understand the assumptions under which Goldstone theorem is valid. Is it just a Lagrangian that depends on scalar fields and has no gauge potentials? Or is it also true for more general Lagrangians?
Given a Lagragian L which contains no gauge bosons and which is invariant under the group G but the ground state is only invariant under the subgroup H, then there exists dim G- dim H Goldstone bosons (massless and spinless).