Journal of High Energy Physics

, Volume 2015, Issue 12, pp 1–33 | Cite as

An algebraic approach to the scattering equations

  • Rijun Huang
  • Junjie RaoEmail author
  • Bo Feng
  • Yang-Hui He
Open Access
Regular Article - Theoretical Physics


We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.


Scattering Amplitudes Differential and Algebraic Geometry Gauge Symmetry 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Rijun Huang
    • 1
  • Junjie Rao
    • 1
    Email author
  • Bo Feng
    • 1
    • 2
  • Yang-Hui He
    • 3
    • 4
    • 5
  1. 1.Zhejiang Institute of Modern PhysicsZhejiang UniversityHangzhouP.R. China
  2. 2.Center of Mathematical ScienceZhejiang UniversityHangzhouP.R. China
  3. 3.School of PhysicsNanKai UniversityTianjinP.R. China
  4. 4.Department of MathematicsCity UniversityLondonU.K.
  5. 5.Merton CollegeUniversity of OxfordOxfordU.K.

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