We propose a new method of constructing the effective theory for a multicomponent low-dimensional dilute Bose gas. The method is based on obtaining and solving renormalization group equations for all many-body interactions of density-density type in the one-loop approximation. In contrast to the standard approach based on two-body interactions, our method does not rely on the introduction of density-dependent infrared cutoff, and is able to reproduce exactly the leading term in the energy density of the one-dimensional dilute Bose gas, and to obtain the next term with the error of less than 2%.

中文翻译：

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一维稀释 Bose 气体中的有效多体相互作用

我们提出了一种构建多组分低维稀释玻色气体有效理论的新方法。该方法基于在单环近似中获得和求解所有密度-密度类型的多体相互作用的重整化群方程。与基于二体相互作用的标准方法相比，我们的方法不依赖于引入与密度相关的红外截止，并且能够准确再现一维稀释 Bose 气体的能量密度的主要项，并得到误差小于 2% 的下一项。