arXiv journal 2022.0217

这两篇论文探讨了量子场论中散射振幅的几何性质。第一篇指出,散射振幅在非导数字段重定义下具有一种类似于张量的'壳上协变性',并提出了一种推广的几何框架来展示这一点。第二篇提出了一种几何-动力学对偶,将任意无质量玻色子理论等效为带有动量依赖的场空间度量的非线性sigma模型,并展示了如何通过几何方法推导出散射振幅。这些发现对于有效场理论有直接的应用,包括软定理的统一表述。

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On-Shell Covariance of Quantum Field Theory Amplitudes
https://arxiv.org/pdf/2202.06965.pdf

abstract: 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.

Geometry-Kinematics Duality
https://arxiv.org/pdf/2202.06972.pdf

abstract: We propose a mapping between geometry and kinematics that implies the classical equivalence of any theory of massless bosons—including spin and exhibiting arbitrary derivative or potential interactions—to a nonlinear sigma model (NLSM) with a momentum-dependent metric in field space. From this kinematic metric we construct a corresponding kinematic connection, covariant derivative, and curvature, all of which transform appropriately under general field redefinitions, even including derivatives. We show explicitly how all tree-level on-shell scattering amplitudes of massless bosons are equal to those of the NLSM via the replacement of geometry with kinematics. Lastly, we describe how the recently introduced geometric soft theorem of the NLSM, which universally encodes all leading and subleading soft scalar theorems, also captures the soft photon theorems.

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