  In accord with Nambu-Goldstone theorem spontaneous breaking of a global
continuous symmetry of the system by a mean-field order parameter causes
appearance of massless Goldstone bosons, called also gapless Goldstone modes.
It is demonstrated below that the theorem can be violated, i.e. the Goldstone
modes possess finite gap, in the case of a novel "Euclidian crystal" (quantum
ordered) state of interacting fermions, that was proposed recently {mukhin
2011}. This result may lead to the important consequences when considered in
combination with another peculiar properties of the quantum order parameter
(QOP) that where recently found: QOP's Green's function is finite and periodic
along the Matsubara's axis, but Wick-rotated to the axis of real frequencies,
possesses infinite periodic "chain" of \it{second order poles} along this axis
{mukhin 2011}. This property of QOP leads to a remarkable physical consequence:
\it{QOP does not scatter anything in Minkowski world} ! Hence, the present
theory, we believe, may naturally indicate that two effects: "hidden order"
revealed in ARPES spectra of fermi-excitations and "neutron resonance" feature
at finite frequency in the magnetic (bosonic) excitations spectrum in lightly
hole-doped copper oxides, could be emerging fingerprints of the Euclidian
crystal state. A peculiar manifestation of the QOP self-consistent solution in
the form of non-classical phonon states is described for an "electromagnetic
Euclidian crystal" predicted recently {mukhin,fistul 2013} in the array of
Josephson junctions coupled via electromagnetic field in the superconducting
resonator. It is demonstrated that it may constitute a stable state of the
system, that, for a particular quantum disordering model, exists inside the
stability domain of the classical photonic condensate delimited by the critical
value of the quantum disordering strength.
