论文标题
Steinmann关系和宇宙的波函数
Steinmann Relations and the Wavefunction of the Universe
论文作者
论文摘要
因果关系和单位性的物理原理对平面S-矩阵的分析结构施加了强烈的限制。特别是，这些原则引起了Steinmann的关系，这要求在部分重叠的动量通道中散射幅度的双重不连续性消失。相反，在宇宙学量表上，因果关系和单位性的烙印通常不那么理解 - 宇宙的波函数一直生活在未来的太空式边界上，并且所有时间的演变都整合在一起。在目前的工作中，我们展示了扁平空间Steinmann的关系如何从宇宙的波函数结构中出现，并得出适用于波函数本身的相似关系。这是在标量玩具模型的背景下完成的，其扰动波函数在宇宙学的多面有方面具有第一原理定义。特别是，我们使用这样一个事实，即散射幅度是在宇宙多型的散射方面编码的，并且幅度的切割被编码在该方面的编码一个边界中。如我们所示，扁平空间Steinmann的关系是由与与部分重叠的通道成对相关的边界的交叉点上的codimension-two边界的不存在所隐含的。将相同的论点应用于完整的宇宙多主体，我们还得出了适用于宇宙全波函数的Steinmann型约束。这些论点表明了宇宙学多型的组合特性如何导致S-Matrix中统一因果关系的出现，并为宇宙波函数的分析结构提供新的见解。
The physical principles of causality and unitarity put strong constraints on the analytic structure of the flat-space S-matrix. In particular, these principles give rise to the Steinmann relations, which require that the double discontinuities of scattering amplitudes in partially-overlapping momentum channels vanish. Conversely, at cosmological scales, the imprint of causality and unitarity is in general less well understood---the wavefunction of the universe lives on the future space-like boundary, and has all time evolution integrated out. In the present work, we show how the flat-space Steinmann relations emerge from the structure of the wavefunction of the universe, and derive similar relations that apply to the wavefunction itself. This is done within the context of scalar toy models whose perturbative wavefunction has a first-principles definition in terms of cosmological polytopes. In particular, we use the fact that the scattering amplitude is encoded in the scattering facet of cosmological polytopes, and that cuts of the amplitude are encoded in the codimension-one boundaries of this facet. As we show, the flat-space Steinmann relations are thus implied by the non-existence of codimension-two boundaries at the intersection of the boundaries associated with pairs of partially-overlapping channels. Applying the same argument to the full cosmological polytope, we also derive Steinmann-type constraints that apply to the full wavefunction of the universe. These arguments show how the combinatorial properties of cosmological polytopes lead to the emergence of flat-space causality in the S-matrix, and provide new insights into the analytic structure of the wavefunction of the universe.
