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Article
Report number	arXiv:2202.06965
Title	On-Shell Covariance of Quantum Field Theory Amplitudes
Author(s)	Cohen, Timothy (Oregon U.) ; Craig, Nathaniel (UC, Santa Barbara) ; Lu, Xiaochuan (Oregon U.) ; Sutherland, Dave (INFN, Trieste ; CERN)
Publication	2023-01-27
Imprint	2022-02-14
Number of pages	6
In:	Phys. Rev. Lett. 130 (2023) 041603
DOI	10.1103/PhysRevLett.130.041603 (publication)
Subject category	Particle Physics - Phenomenology ; Particle Physics - Theory
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.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2023-2025 authors (License: CC BY 4.0), sponsored by SCOAP³

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