Bose condensation : one-particle excitations, chemical potential and theorem for averages

A new description of systems with Bose condensate is presented. The temperature Tc of transition to the state with a condensate is defined from the condition of the appearance of a singularity in the one-particle Green's function. The properties of a condensed state are fully determined by the condition of equality between the chemical potential and the minimal value of the spectrum of the one-particle excitations for T <Tc. As a consequence of this condition the usual (non-gap-like) dependence of the specific heat on the temperature is recovered for T <Tc. The generalized Wick theorem for averages is formulated, which permits to use the standard diagram technique for Bose condensed systems. A model of the system with d(r) potential for interaction is considered in Hartree-Fock approximation for T <Tc. The possibility of the existence of the two different branches of excitations is discussed in relation with two different functions: the one-particle Green's function with a gap and the density-density correlation function corresponding to the usually measured phonon-roton branch.