Amplituhedra, and beyond. (29th December 2020)

• Record Type: Journal Article
• Authors: Ferro, Livia; Łukowski, Tomasz
• Is Part Of: Journal of physics. Volume 54:Number 3(2021)
• Publication Date: 2020-12-29
• Subjects: scattering amplitudes in maximally supersymmetric Yang–Mills theory -- scattering amplitudes in scalar cubic theory -- positive geometries for amplitudes; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/abd21d
• Languages: English
• ISSNs: 1751-8113

Abstract

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.