We present a renormalized theory which is free of the infrared (IR) divergences for Bose-Einstein-condensed systems. It is shown that the Beliaev-Dyson equation can be made regular in the IR limit by expressing the Green functions in the form of a series starting from the Bogiliubov approximation. In the resulting equations for Green's functions, all IR divergences are removed completely due to the appearance of natural IR cutoff factors. Our theory is applied to a low-density Bose gas, where we calculate the first three terms in the series expansion of the ground-state energy and chemical potential.

中文翻译：

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Bose-Einstein凝聚系统Beliaev-Dyson方程中红外散度的消除

我们提出了一种重归一化的理论，该理论没有针对Bose-Einstein凝聚系统的红外（IR）发散。结果表明，通过从Bogiliubov逼近开始，以一系列的形式表示Green函数，可以使Beliaev-Dyson方程在IR极限中规则化。在格林函数的最终方程中，由于出现了自然的红外截止因子，所有的红外散度都被完全消除了。我们的理论适用于低密度Bose气体，我们在其中计算基态能量和化学势的级数展开的前三个项。