摘要
Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） 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 Schroedinger eigenvalue equation and using the self-consistent condition.
Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） 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 Schroedinger eigenvalue equation and using the self-consistent condition.
基金
0ne of author （Huang H B） was partially supported by the Natural Science Foundation of Jiangsu province, China （Grant No BK2005062）.Acknowledgement We thank Professor Tian G S for discussion
