论文标题
部分可观测时空混沌系统的无模型预测
Gauge invariance from on-shell massive amplitudes and tree unitarity
论文作者
论文摘要
我们通过采用内壳巨大的纺纱形式，研究了任意数量的大量标量，旋转器和向量的三粒子和四粒子散射幅度。我们认为最通用的三粒子振幅具有大多数$ \ Mathcal {o}（e）$的能量生长行为。这是树木单位性要求的特殊情况，它指出，在高能硬散射极限，即以固定的非零角度，在高能量硬散射极限中，树水平的$ n $ - 粒子散射幅度最多应以$ \ Mathcal {O}（E^{4-N}）$。然后，通过将壳上的三颗粒幅度粘合在一起，并利用树级振幅仅具有简单的极点来计算四粒子振幅的可分化部分。四粒子振幅的接触部分通过树木单位性进一步确定，这也对允许的三粒子耦合常数和质量构成了强大的限制。它们之间的派生关系融合了紫外线理论中规范不变性的预测。这纯粹是对自发损坏的理论的壳理解。
We study the three-particle and four-particle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the on-shell massive spinor formalism. We consider the most general three-particle amplitudes with energy growing behavior at most of $\mathcal{O} (E)$. This is the special case of the requirement of tree unitarity, which states that the $N$-particle scattering amplitudes at tree-level should grow at most as $\mathcal{O} (E^{4-N})$ in the high energy hard scattering limit, i.e. at fixed non-zero angles. Then the factorizable parts of the four-particle amplitudes are calculated by gluing the on-shell three-particle amplitudes together and utilizing the fact that tree-level amplitudes have only simple poles. The contact parts of the four-particle amplitudes are further determined by tree unitarity, which also puts strong constraints on the possible allowed three-particle coupling constants and the masses. The derived relations among them converge to the predictions of gauge invariance in the UV theory. This provides a purely on-shell understanding of spontaneously broken gauge theories.
