The momentum amplituhedron

  • David Damgaard
  • Livia Ferro
  • Tomasz LukowskiEmail author
  • Matteo Parisi
Open Access
Regular Article - Theoretical Physics


In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in \( \mathcal{N} \) = 4 super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron Mn,k is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.


Scattering Amplitudes Supersymmetric Gauge Theory 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • David Damgaard
    • 1
  • Livia Ferro
    • 1
    • 2
  • Tomasz Lukowski
    • 2
    Email author
  • Matteo Parisi
    • 3
  1. 1.Arnold-Sommerfeld-Center for Theoretical PhysicsLudwig-Maximilians-UniversitätMünchenGermany
  2. 2.School of Physics, Astronomy and MathematicsUniversity of HertfordshireHertfordshireU.K.
  3. 3.Mathematical InstituteUniversity of OxfordOxfordU.K.

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