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We analyze the group-theoretical ramifications of the Nambu-Goldstone [NG]theorem in the self-consistent relativistic variational Gaussian wavefunctional approximation to spinless field theories. In an illustrative examplewe show how the Nambu-Goldstone theorem would work in the O(N) symmetric$\phi^4$ scalar field theory, if the residual symmetry of the vacuum werelesser than O(N-1), e.g. if the vacuum were O(N-2), or O(N-3),... symmetric.[This does not imply that any of the "lesser" vacua is actually the absoluteenergy minimum: stability analysis has not been done.] The requisite number ofNG bosons would be (2N - 3), or (3N - 6), ... respectively, which may exceed N,the number of elementary fields in the Lagrangian. We show how the requisitenew NG bosons would appear even in channels that do not carry the same quantumnumbers as one of N "elementary particles" (scalar field quanta, orCastillejo-Dalitz-Dyson [CDD] poles) in the Lagrangian, i.e. in those "flavour"channels that have no CDD poles. The corresponding Nambu-Goldstone bosons arecomposites (bound states) of pairs of massive elementary (CDD) scalar fieldsexcitations. As a nontrivial example of this method we apply it to thephysically more interesting 't Hooft $\sigma$ model (an extended $N_{f} = 2$bosonic linear $\sigma$ model with four scalar and four pseudoscalar fields),with spontaneously and explicitly broken chiral $O(4) \times O(2) \simeqSU_{\rm R} (2) \times SU_{\rm L}(2) \times U_{\rm A}(1)$ symmetry.Comment: 17 pages, no figure

Dynamical symmetry breaking and the Nambu–Goldstone theorem in the Gaussian wave functional approximation