  We analyze the group-theoretical ramifications of the Nambu-Goldstone [NG]
theorem in the self-consistent relativistic variational Gaussian wave
functional approximation to spinless field theories. In an illustrative example
we 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 were
lesser 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 absolute
energy minimum: stability analysis has not been done.] The requisite number of
NG 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 requisite
new NG bosons would appear even in channels that do not carry the same quantum
numbers as one of N "elementary particles" (scalar field quanta, or
Castillejo-Dalitz-Dyson [CDD] poles) in the Lagrangian, i.e. in those "flavour"
channels that have no CDD poles. The corresponding Nambu-Goldstone bosons are
composites (bound states) of pairs of massive elementary (CDD) scalar fields
excitations. As a nontrivial example of this method we apply it to the
physically 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 $O(4) \times O(2) \simeq
SU_{\rm R} (2) \times SU_{\rm L}(2) \times U_{\rm A}(1)$ symmetry.
