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تسجيل مستخدم جديدAmplituhedra, and Beyond
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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.
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Recently, the existence of an Amplituhedron for tree level amplitudes in the bi-adjoint scalar field theory has been proved by Arkhani-Hamed et al. We argue that hyperbolic geometry constitutes a natural framework to address the study of positive geo
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Any totally positive $(k+m)times n$ matrix induces a map $pi_+$ from the positive Grassmannian ${rm Gr}_+(k,n)$ to the Grassmannian ${rm Gr}(k,k+m)$, whose image is the amplituhedron $mathcal{A}_{n,k,m}$ and is endowed with a top-degree form called t
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