论文标题
S-Matrix Bootstrap的分析工具包
An Analytical Toolkit for the S-matrix Bootstrap
论文作者
论文摘要
我们重新审视分析方法，用于限制统一，相对论，间隔理论的非扰动$ s $ matrix $ d \ geq 3 $时空维度。我们假设两到两个散射幅度的扩展分析性，并将其与弹性单位性一起使用，以发展幅度的两个自然膨胀。一个是阈值（非偏见）膨胀，另一个是较大的自旋膨胀。两者与Froissart-Gribov倒置公式相关。当与振幅不连续性的交叉和局部结合结合时，这使我们能够根据实验中测得的低能参数来限制有限能量和自旋的散射。最后，我们讨论了$ S $ -Matrix引导程序的现代数值方法，以及如何根据分析结果将其改进。
We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $d \geq 3$ spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it together with elastic unitarity to develop two natural expansions of the amplitude. One is the threshold (non-relativistic) expansion and the other is the large spin expansion. The two are related by the Froissart-Gribov inversion formula. When combined with crossing and a local bound on the discontinuity of the amplitude, this allows us to constrain scattering at finite energy and spin in terms of the low-energy parameters measured in the experiment. Finally, we discuss the modern numerical approach to the $S$-matrix bootstrap and how it can be improved based on the results of our analysis.
