  We consider the self-evolution of strongly non-equilibrium interacting Bose
gas. Due to the mere fact of large (as compared to unity) occupation numbers in
the initial state the problem is directly reduced to the question of temporal
evolution of the statistical matrix diagonal in the coherent-state
representation.
  Strictly speaking, gauge symmetry is not destroyed even when the long-range
ordering is completed, owing to the ineviatble averaging over the ensemble.
Actual symmetry breaking can occur only as a result of introducing a small term
of the Hamiltonian violating conservation of particles, or quantum-mechanical
measurement, also implying non-conservation of particles.
