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We consider the self-evolution of strongly non-equilibrium interacting Bosegas. Due to the mere fact of large (as compared to unity) occupation numbers inthe initial state the problem is directly reduced to the question of temporalevolution of the statistical matrix diagonal in the coherent-staterepresentation.  Strictly speaking, gauge symmetry is not destroyed even when the long-rangeordering is completed, owing to the ineviatble averaging over the ensemble.Actual symmetry breaking can occur only as a result of introducing a small termof the Hamiltonian violating conservation of particles, or quantum-mechanicalmeasurement, also implying non-conservation of particles.Comment: Revtex, 5 pages, no figures. To be published in Phys. Rev. Let

Evolution of Correlation Properties and Appearance of Broken Symmetry in the Process of Bose-Einstein Condensation