论文标题
相对论三粒子量化条件的替代推导
Alternative derivation of the relativistic three-particle quantization condition
论文作者
论文摘要
我们提出了相对论三粒子量化条件的简化推导，该条件是通过满足$ \ mathbb z_2 $对称性的一般相对论场理论所描述的相同无旋转粒子的。简化是通过使用未完全对称的三粒子式k矩阵，$ \ widetilde {\ Mathcal {k}} _ {\ rm df，3}^{（u，u，u）} $，并进行了广泛的使用时间范围的扰动理论（TOPT）。我们获得了一种新形式的量化条件。然后，这种新表单可以与标准量化条件相关，该标准量化条件取决于完全对称的三粒子k矩阵，$ \ nathcal {k} _ {\ rm df，3} $。新的推导是完全明确的，例如，允许以$ \ Mathcal {k} _ {\ rm df，3} $的封闭形式表达式，以TOPT幅度给出。量化条件的新形式的结构与“有限体积单位性”方法中获得的结构相似，在伴随纸中，我们使这种连接混凝土。我们的简化方法还应使量化条件更直接地概括为非成型颗粒，也许还可以对三个以上的粒子进行概括。
We present a simplified derivation of the relativistic three-particle quantization condition for identical, spinless particles described by a generic relativistic field theory satisfying a $\mathbb Z_2$ symmetry. The simplification is afforded by using a three-particle quasilocal K matrix that is not fully symmetrized, $\widetilde{\mathcal{K}}_{\rm df,3}^{(u,u)}$, and makes extensive use of time-ordered perturbation theory (TOPT). We obtain a new form of the quantization condition. This new form can then be related algebraically to the standard quantization condition, which depends on a fully symmetric three-particle K matrix, $\mathcal{K}_{\rm df,3}$. The new derivation is fully explicit, allowing, for example, a closed-form expression for $\mathcal{K}_{\rm df,3}$ to be given in terms of TOPT amplitudes. The new form of the quantization condition is similar in structure to that obtained in the "finite-volume unitarity" approach, and in a companion paper we make this connection concrete. Our simplified approach should also allow a more straightforward generalization of the quantization condition to nondegenerate particles, and perhaps also to more than three particles.
