Faddeev方程与三玻色子系统低能短程有效场论研究  

Faddeev equation for three-boson system in low-energy short-distance effective field theory

作　　者：王凯[1] 杨继锋[1] WANG Kai;YANG Jifeng(School of Physics and Electronic Science,East China Normal University,Shanghai 200241,China)

机构地区：[1]华东师范大学物理与电子科学学院,上海200241

出　　处：《华东师范大学学报（自然科学版）》2023年第4期137-150,共14页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11435005)。

摘　　要：在低能短程(接触型势能)有效场论中二体t矩阵闭合形式解的基础上,用Faddeev方程计算了二体接触型势能前提下的零自旋三玻色子系统三体T矩阵的闭合形式近似解.在动量表示里接触型势能是多项式,其二体t矩阵满足的Lippmann-Schwinger方程可用因子化方法约化为闭合的代数方程,从而可得到该方程的解析解,并方便地对其进行非微扰重整化.但是在Faddeev方程中难以直接沿用上述因子化方法.为此,对三体T矩阵元的外动量依赖采用“分流”处理,从而仍可利用因子化方法将Faddeev方程转化为代数方程.在此基础上求得了领头阶二体势能下的三体T矩阵的闭合形式近似解,并推广到次领头阶势能下的情形,进而完成了自洽性验证.与二体问题一样,由于因子化和一般参数化,这样的三体T矩阵非微扰解析解同样可以允许方便地进行非微扰重整化.Based on the closed-form t matrix of a two-body system in low-energy short-distance effective field theory,the approximate closed-form three-body T matrix for a zero-spin three-boson system is obtained using the Faddeev equation under two-body contact interactions.In momentum representation,the contact potentials are polynomials,and the Lippmann-Schwinger equation can be simplified to algebraic equations using a factorization trick,facilitating nonperturbative renormalization.However,it is impossible to apply such a factorization trick directly to the Faddeev equation.Therefore,the momenta dependence of the T matrix is“split”such that the factorization trick can still be applied.The closed-form T matrices are then obtained as nonperturbative approximate solutions of the Faddeev equation under the leading and next-to-leading order contact potentials with verified consistency.As in a two-body case,such a closed-form T matrix also facilitates the convenient implementation of the nonperturbative renormalization.

关 键 词：有效场论 Faddeev方程 非微扰近似 一般参数化 

分 类 号：O413.3[理学—理论物理]