论文标题
量子场理论振幅的壳上协方差
On-Shell Covariance of Quantum Field Theory Amplitudes
论文作者
论文摘要
量子场理论中的散射幅度与场参数化无关，该参数化具有自然的几何解释作为“坐标不变性”的一种形式。幅度可以用riemannian曲率张量表示，这使得在非衍生场重新定义的情况下振幅的协方差显现出来。我们提出了一个广义的几何框架，该框架将这种明显的协方差扩展到$ $ $允许的字段重新定义。幅度满足了递归关系，该关系与协方差衍生物的应用非常相似，以增加张量的排名。这使我们可以说（树级）幅度具有“壳协方差”的概念，因为它们在任何允许的场下都会转换为张量，直到施加运动方程和壳上的动量约束时消失的一组术语。我们重点介绍了有效的现场理论的各种直接应用。
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature tensors, which makes the covariance of amplitudes under non-derivative field redefinitions manifest. We present a generalized geometric framework that extends this manifest covariance to $all$ allowed field redefinitions. Amplitudes satisfy a recursion relation that closely resembles the application of covariant derivatives to increase the rank of a tensor. This allows us to argue that (tree-level) amplitudes possess a notion of `on-shell covariance,' in that they transform as a tensor under any allowed field redefinition up to a set of terms that vanish when the equations of motion and on-shell momentum constraints are imposed. We highlight a variety of immediate applications to effective field theories.
