The Casimir effect in a dilute Bose gas confined between two parallel plates is investigated at zero temperature by means of Cornwall–Jackiw–Tomboulis effective action approach within the improved Hartree–Fock approximation in the canonical ensemble, in which the particle number is fixed. In comparison with those in the grand canonical ensemble, where the particle number can be changed, the fixation of the particle number leads to the significant changes in the Casimir energy and the resulting Casimir force. The most interesting result is that the Casimir energy and Casimir force decay in accordance with a half-integer power law instead of an integer power law in the grand canonical ensemble. Moreover, the scattering length dependence of the Casimir force is also considered.

在改进的Hartree-Fock近似中，采用固定的粒子数，通过康沃尔-杰基-通布利斯有效作用方法，在零温度下研究了封闭在两个平行板之间的稀玻色气体中的卡西米尔效应。与大正则合奏中的粒子数可以更改的情况相比，粒子数的固定会导致卡西米尔能量和所产生的卡西米尔力发生重大变化。最有趣的结果是，卡西米尔能量和卡西米尔力按照大整数幂律而不是整数幂律衰减，而是按照半整数幂定律衰减。此外，还考虑了卡西米尔力的散射长度依赖性。