具有任意分波含量的自旋1/2费米子多体系统的阶梯重算
Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content
摘要：
本文用任意真空两体散射振幅计算自旋1/2费米子多体系统的能量密度$\cal{E}$。本文提出了介质中两体散射振幅的分波分解，并给出了分波振幅展开中计算$\cal{E}$的表达式。接触相互作用的情况下完全解决，并提供重整化的结果，直接表示在散射数据参数，在广泛的一类计划中的截止正则化。考虑$S$ -和$P$ -波相互作用，直至包括有效范围扩展中的前三项，特别注意么正极限周围的参数区域。
英文摘要：
We resum the ladder diagrams for the calculation of the energy density $\cal{E}$ of a spin 1/2 fermion many-body system in terms of arbitrary vacuum two-body scattering amplitudes. The partial-wave decomposition of the in-medium two-body scattering amplitudes is developed, and the expression for calculating $\cal{E}$ in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved and is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. $S$- and $P$-wave interactions are considered up to including the first three-terms in the effective-range expansion, paying special attention to the parametric region around the unitary limit.
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