University of Hertfordshire

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Amplituhedra, and Beyond

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Original languageEnglish
Article number033001
Number of pages43
JournalJournal of Physics A: Mathematical and Theoretical
Early online date29 Dec 2020
Publication statusE-pub ahead of print - 29 Dec 2020


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.


© 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 ( Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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