On-shell covariance of quantum field theory amplitudes

Cohen, T., Craig, N., Lu, X. and Sutherland, D. (2023) On-shell covariance of quantum field theory amplitudes. Physical Review Letters, 130(4), 041603. (doi: 10.1103/PhysRevLett.130.041603)

Abstract

Scattering amplitudes in quantum field theory are independent of the field parametrization, 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 nonderivative field redefinitions manifest. We present a generalized geometric framework that extends this manifest covariance to all allowed field redefinitions. Amplitudes satisfy a recursion relation to all orders in perturbation theory 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Sutherland, Dr David
• Authors: Cohen, T., Craig, N., Lu, X., and Sutherland, D.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: Physical Review Letters
• Publisher: American Physical Society
• ISSN: 0031-9007
• ISSN (Online): 1079-7114
• Copyright Holders: Copyright © 2023 American Physical Society
• First Published: First published in Physical Review Letters 130(4): 041603
• Publisher Policy: Reproduced under a Creative Commons License

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