Spontaneous U(1) symmetry breaking and Bose–Einstein condensation

Abstract

Based on Bogoliubov's truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U(1) symmetry breaking term V1/2(λa0+λ*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 Schrodinger eigenvalue equation and using the self-consistent condition.