The SAGEX review on scattering amplitudes Chapter 7: Positive geometry of scattering amplitudes

Herrmann, Enrico; Trnka, Jaroslav

doi:10.1088/1751-8121/ac8709

The SAGEX review on scattering amplitudes Chapter 7: Positive geometry of scattering amplitudes

Journal Article · 04 November 2022 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/ac8709· OSTI ID:2419894

^[1]; Trnka, Jaroslav

OSTI

Abstract

Scattering amplitudes are both a wonderful playground to discover novel ideas in quantum field theory and simultaneously of immense phenomenological importance to make precision predictions for e.g. particle collider observables and more recently also for gravitational wave signals. In this review chapter, we give an overview of some of the exciting recent progress on reformulating QFT in terms of mathematical, geometric quantities, such as polytopes, associahedra, Grassmanians, and the amplituhedron. In this novel approach, standard notions of locality and unitarity are derived concepts rather than fundamental ingredients in the construction which might give us a handle on a number of open questions in QFT that have evaded an answer for decades. We first give a basic summary of positive geometry before discussing the associahedron—one of the simplest physically relevant geometric examples—and its relation to tree-level scattering amplitudes in bi-adjointϕ³theory. Our second example is the amplituhedron construction for scattering amplitudes in planar maximally supersymmetric Yang–Mills theory.

Research Organization:: Univ. of California, Los Angeles, CA (United States); Univ. of California, Davis, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0009937; SC0009999

OSTI ID:: 2419894

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 44 Vol. 55; ISSN 1751-8113

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

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