标题： 散射振幅的正性性质 显示英文标题

标题： Positivity properties of scattering amplitudes

摘要： 我们研究量子场论（QFT）中的正性性质。 我们发现QFT中的平面费曼积分以及许多相关量满足无限多个正性条件：在指定的运动学区域内，这些函数及其所有带符号导数都是非负的。 这些函数在数学文献中被称为完全单调（CM）。 通过积分表示是一种认证完全单调性的有力方法。 因此，我们证明它适用于具有欧几里得区域的非平面积分、宇宙相关函数以及某些弦论积分。 受正几何的启发，我们研究平面极大超对称杨-米尔斯理论中的正性性质。 我们提出证据，基于已知的解析多环结果，表明CM性质扩展到该理论中的几个物理量。 这包括六粒子最大螺旋度破坏（MHV）振幅的适当归一化的有限余项函数、库仑分支上的四点散射振幅、四点关联函数，以及角度相关的尖点异常维数。 然而，我们的发现并不局限于超对称理论。 结果显示，CM性质分别在QCD和QED的尖点异常维数中成立，分别到三环和四环。 我们评论了开放的问题，以及完全单调性的可能数值应用。 显示英文摘要

摘要： We investigate positivity properties in quantum field theory (QFT). We find that planar Feynman integrals in QFT, as well as many related quantities, satisfy an infinite number of positivity conditions: the functions, as well as all their signed derivatives, are non-negative in a specified kinematic region. Such functions are known as completely monotonic (CM) in the mathematics literature. A powerful way to certify complete monotonicity is via integral representations. We thus show that it applies to non-planar integrals possessing a Euclidean region, to cosmological correlators, as well as to certain stringy integrals. Motivated by Positive Geometry, we investigate positivity properties in planar maximally supersymmetric Yang-Mills theory. We present evidence, based on known analytic multi-loop results, that the CM property extends to several physical quantities in this theory. This includes the (suitably normalized) finite remainder function of the six-particle maximally-helicity violating (MHV) amplitude, four-point scattering amplitudes on the Coulomb branch, four-point correlation functions, as well as the angle-dependent cusp anomalous dimension. Our findings are however not limited to supersymmetric theories. It is shown that the CM property holds for the QCD and QED cusp anomalous dimensions, to three and four loops, respectively. We comment on open questions, and on possible numerical applications of complete monotonicity.