相对论三粒子量子化条件的另一种推导
Alternative derivation of the relativistic three-particle quantization condition
摘要：
我们提出了一个简化推导的相对论性三粒子量子化条件相同，无自旋粒子描述的一般相对论性场论满足$\mathbb Z_2$对称性。通过使用不完全对称的三粒子准局部K矩阵$\widetilde{\mathcal{K}}_{\rm df,3}^{(u,u)}$，并广泛使用时间有序微扰理论（TOPT），提供了简化。我们得到了量子化条件的一种新形式。这个新的形式可以与标准量子化条件代数相关，标准量子化条件依赖于完全对称的三粒子K矩阵$\mathcal{K}_{\rm df,3}$。新的推导是完全明确的，允许，例如，一个封闭形式的表达式$\mathcal{K}_{\rm df,3}$的TOPT振幅。量子化条件的新形式在结构上类似于在“有限体积么正性”方法中得到的量子化条件，在一篇配套文章中，我们将使这种联系具体化。我们的简化方法也应该允许量子化条件更直接地推广到非简并粒子，也许也可以推广到三个以上的粒子。
英文摘要：
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.
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