【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.更多还原

【Abstract】 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.更多还原