Casimir force of a dilute Bose gas confined by a parallel plate geometry in improved Hatree-Fock approximation

Within framework of quantum field theory, in improved Hatree-Fock (IHF) approximation, we have considered a dilute single Bose-Einstein condensate (BEC) confined between two parallel plates. We found that the effective mass and order parameter of BEC strongly depend on distance separating two plates. Our results shows that the effective mass, order parameter and the Casimir force in IHF approximation equal to their values in one-loop approximation added a corrected term due to contribution of two-loop diagrams. We also show that the one-loop approximation is enough for calculating Casimir effect in an ideal Bose gas.