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Based on Bogoliubov's truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U(1) symmetry breaking term $\sqrt{V}(\lambda a0+\lambda*a0+) 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. 相似文献
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