近日，英国诺丁汉大学物理与天文学院的Zong-Zhe Du与David Stefanyszyn合作并取得一项新进展。经过不懈努力，他们提出无变换振幅的软定理。相关研究成果已于2024年7月2日在国际知名学术期刊《高能物理杂志》上发表。
该研究团队考虑具有破缺洛伦兹变换的标量场的有效场论(EFT)，它是通过对膨胀EFT解耦和平面空间极限而产生的，并推导出如果存在潜在的非线性实现对称，则相应的散射振幅必须满足的约束。研究人员主要关注依赖于时空坐标的扩展移位对称性，并发现散射振幅的组合服从增强的阿德勒零条件。也就是说，当一个外部动量变弱时，这种组合就会消失，它们消失的速度由相应的对称性决定。
在本文软定理推导中，研究人员聚焦于由于时空平移而产生的能量和动量守恒的δ函数，并表明当对空间动量的导数起作用时，它们产生了一堆软定理，这些软定理最终需要对底层对称代数进行闭包。所有的软定理都对应于壳上振幅必须满足的约束，甚至对于依赖于时间坐标的对称性，该研究提出的软定理只要求对空间动量求导。研究人员通过软自举过程来找到软定理的解，并将这些解与他们使用协集构造从离壳分析中得到的解进行比较。
附：英文原文
Title: Soft theorems for boostless amplitudes
Author: Du, Zong-Zhe, Stefanyszyn, David
Issue&Volume: 2024-07-02
Abstract: We consider effective field theories (EFTs) of scalar fields with broken Lorentz boosts, which arise by taking the decoupling and flat-space limits of the EFT of inflation, and derive constraints that must be satisfied by the corresponding scattering amplitudes if there is an underlying non-linearly realised symmetry. We primarily concentrate on extended shift symmetries which depend on the space-time coordinates, and find that combinations of scattering amplitudes obey enhanced Adler zeros. That is, such combinations vanish as one external momentum is taken soft, with the rate at which they vanish dictated by the corresponding symmetry. In our soft theorem derivation, we pay particular care to the energy and momentum-conserving delta functions that arise due to space-time translations, and show that when acted upon by derivatives with respect to spatial momenta, they yield a tower of soft theorems which are ultimately required for closure of the underlying symmetry algebra. All of our soft theorems correspond to constraints that must be satisfied by on-shell amplitudes and, even for symmetries that depend on the time coordinate, our soft theorems only require derivatives to be taken with respect to spatial momenta. We perform a soft bootstrap procedure to find solutions to our soft theorems, and compare these solutions to what we find from an off-shell analysis using the coset construction.
DOI: 10.1007/JHEP07(2024)011
Source: https://link.springer.com/article/10.1007/JHEP07(2024)011