The Hohenberg–Martin dilemma of conserving versus gapless theories for systems with Bose–Einstein condensate is considered. This dilemma states that, generally, a theory characterizing a system with broken global gauge symmetry, which is necessary for Bose–Einstein condensation, is either conserving, but has a gap in its spectrum, or is gapless, but does not obey conservation laws. In other words, such a system either displays a gapless spectrum, which is necessary for condensate existence, but is not conserving, which implies that it corresponds to an unstable system, or it respects conservation laws, describing a stable system, but the spectrum acquires a gap, which means that the condensate cannot appear. An approach is described, resolving this dilemma, and it is shown to give good quantitative agreement with experimental data. Calculations are accomplished in the Hartree–Fock–Bogolubov approximation.

中文翻译：

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玻色凝聚系统理论中的Hartree-Fock-Bogolubov方法

考虑了玻色-爱因斯坦冷凝物系统的守恒理论与无间隙理论的Hohenberg-Martin困境。这种两难境地表明，一般而言，对于玻色-爱因斯坦凝聚所必需的具有破坏的全局规范对称性的系统进行表征的理论要么守恒，要么谱上有缺口，要么是无隙的，但不遵守守恒定律。换句话说，这样的系统要么显示出无间隙的光谱（这对于冷凝物的存在是必需的），但不是守恒的，这意味着它对应于一个不稳定的系统，或者它遵循守恒律，描述了一个稳定的系统，但是光谱获得了间隙，这意味着不会出现冷凝水。描述了一种解决这一难题的方法，并表明该方法与实验数据具有良好的定量一致性。