Abstract Based on Bogoliubov's truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U(1) symmetry breaking term $\sqrt{V}(\lambda a_0+\lambda^* a_0^+)$ to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose--Einstein condensation(BEC) occurs if and only if the U(1) symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schr\"{o}dinger eigenvalue equation and using the self-consistent condition.
Received: 03 July 2005
Revised: 09 November 2005
Accepted manuscript online:
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