稀薄相互作用玻色气体：费曼图展开与虚时格林函数层级方程的比较
The dilute interacting Bose gas : comparisons between Feynman diagrammatic expansion and the hierarchy equations for the imaginary time Green functions
AI总结：
本文比较了描述相互作用玻色气体的费曼图展开与虚时格林函数层级方程两种形式体系，证明Hartree-Fock近似及其低密度修正可等价表述，并展示了层级方法中两体关联的最低阶表示，为计算更高阶修正开辟了途径。
摘要：
我们分析了描述相互作用玻色气体的两种形式体系之间的对应关系，即一方面为标准费曼图展开，另一方面为虚时格林函数的层级方程。我们证明了Hartree-Fock近似及其由Baym等人[Eur. Phys. J. B, 24, pp. 107-124 (2001)]导出的低密度下的首阶修正，可以在两种形式体系中等价地表述。在层级方法中，两体关联${\mathcal G}^{(2,\rm T)}$在相互作用的最低阶上以完整单体格林函数表示。这阐明了Hartree-Fock理论修正的物理内容。此外，${\mathcal G}^{(2,\rm T)}$的这种表示可以推广到更高阶，为当密度增加时系统性地计算理想临界温度的进一步修正开辟了道路。
英文摘要：
We analyze the correspondence between two formalisms describing an interacting Bose gas, namely the standard Feynman diagrammatic expansion on the one hand, and the hierarchy equations for the imaginary-time Green functions on the other hand. We show that the Hartree-Fock approximation, as well as its first corrections at low density derived by Baym et al. [Eur. Phys. J. B, 24, pp. 107-124 (2001)], can be equivalently formulated in both formalisms. Within the hierarchy approach, the two-body correlations ${\mathcal G}^{(2,\rm T)}$ are expressed at lowest order in the interactions in terms of the full one-body Green function. This sheds light on the physical content of the corrections to the Hartree-Fock theory. Moreover, this representation of ${\mathcal G}^{(2,\rm T)}$ can be extended to higher orders, opening the way to systematic calculations of further corrections to the ideal critical temperature when the density increases.
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