标题： 热带幅度对于带色拉格朗日量 显示英文标题

标题： Tropical Amplitudes For Colored Lagrangians

摘要： 最近，基于动量数据空间中的简单组合思想，为Tr($\Phi^3$)理论中的散射振幅提出了一个新的公式。这使得所有环数的积分振幅都可以用“曲线积分”来表示，这些积分是使用“头灯函数”这种热带构建块定义的。本文展示了该公式的扩展如何适用于更一般的拉格朗日量的振幅。我们将介绍多种引入热带“分子函数”的方法，使我们能够描述一般的拉格朗日量相互作用。这些“热带分子”的最简单的族计算具有无限多相互作用的有趣拉格朗日量的振幅。我们还描述了用于对一般拉格朗日量的振幅进行热带表述的方法。一种方法是使用“Wick收缩”的变体，将一般相互作用顶点的分子因子粘合在一起。另一种方法是利用表面上多边形的自然特征，给出与任意阶数相互作用相关的所有可能图的新组合描述。 显示英文摘要

摘要： Recently a new formulation for scattering amplitudes in Tr($\Phi^3$) theory has been given based on simple combinatorial ideas in the space of kinematic data. This allows all-loop integrated amplitudes to be expressed as ''curve integrals'' defined using tropical building blocks - the ''headlight functions''. This paper shows how the formulation extends to the amplitudes of more general Lagrangians. We will present a number of different ways of introducing tropical ''numerator functions'' that allow us to describe general Lagrangian interactions. The simplest family of these ''tropical numerators'' computes the amplitudes of interesting Lagrangians with infinitely many interactions. We also describe methods for tropically formulating the amplitudes for general Lagrangians. One uses a variant of ''Wick contraction'' to glue together numerator factors for general interaction vertices. Another uses a natural characterization of polygons on surfaces to give a novel combinatorial description of all possible diagrams associated with arbitrary valence interactions.