Self-consistent equation of state for a weakly non-ideal Bose gas

The properties of a Bose gas at low temperature are investigated by means of a rigorous theoretical analysis of a simple model. On the basis of the viral theorem and the dimensionality theory it is shown that the standard procedure of describing such system by using the c-numbers approximation for the creation and annihilation operators for particles with zero momentum at temperatures T<Tλ, is not correct. The chemical potential and other thermodynamic functions of a weakly non-ideal Bose gas are found by methods involving self-consistent equations.