Amplituhedra, and Beyond

Livia Ferro; Tomasz Lukowski

doi:10.1088/1751-8121/abd21d

Amplituhedra, and Beyond

Livia Ferro, Tomasz Lukowski

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Abstract

This review is a primer on recently established geometric methods for observables in quantum field theories. The main emphasis is on amplituhedra, i.e. geometries encoding scattering amplitudes for a variety of theories. These pertain to a broader family of geometries called positive geometries, whose basics we review. We also describe other members of this family that are associated with different physical quantities and briefly consider the most recent developments related to positive geometries. Finally, we discuss the main open problems in the field. This is a Topical Review invited by Journal of Physics A: Mathematical and Theoretical.

Original language	English
Article number	033001
Number of pages	43
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	54
Issue number	3
Early online date	29 Dec 2020
DOIs	https://doi.org/10.1088/1751-8121/abd21d
Publication status	E-pub ahead of print - 29 Dec 2020

Keywords

Positive geometries for amplitudes
Scattering amplitudes in maximally supersymmetric Yang-Mills theory
Scattering amplitudes in scalar cubic theory

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10.1088/1751-8121/abd21dLicence: CC BY

Ferro_2021_J_54_033001
© 2020 The Author(s). Published by IOP Publishing Ltd. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence (https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Final published version, 1.33 MBLicence: CC BY

Cite this

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Amplituhedra, and Beyond

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