Density of condensate of a dilute Bose gas in improved Hartree-Fock approximation

In a manner of Cornwal-Jackiw-Tomboulis effective action approach, the density of condensate of a dilute Bose gas confined between two planar walls is investigated within the framework of improved Hartree-Fock. Thereby, the quantum fluctuations are taken into account with presence of high-order terms in the momentum integrals. Our results show that the quantum fluctuations significantly belittle the density of condensate compared with square of the expectation value of the field operator. The comparison with relating results of Gross-Pitaevskii theory is made.