Journal of High Energy Physics

, 2016:75 | Cite as

Syzygies probing scattering amplitudes

  • Gang Chen
  • Junyu Liu
  • Ruofei Xie
  • Hao Zhang
  • Yehao Zhou
Open Access
Regular Article - Theoretical Physics


We propose a new efficient algorithm to obtain the locally minimal generating set of the syzygies for an ideal, i.e. a generating set whose proper subsets cannot be generating sets. Syzygy is a concept widely used in the current study of scattering amplitudes. This new algorithm can deal with more syzygies effectively because a new generation of syzygies is obtained in each step and the irreducibility of this generation is also verified in the process. This efficient algorithm can also be applied in getting the syzygies for the modules. We also show a typical example to illustrate the potential application of this method in scattering amplitudes, especially the Integral-By-Part(IBP) relations of the characteristic two-loop diagrams in the Yang-Mills theory.


Differential and Algebraic Geometry Scattering Amplitudes 


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) 2016

Authors and Affiliations

  • Gang Chen
    • 1
    • 2
  • Junyu Liu
    • 3
    • 4
  • Ruofei Xie
    • 2
  • Hao Zhang
    • 2
  • Yehao Zhou
    • 3
    • 4
  1. 1.Department of PhysicsZhejiang Normal UniversityJinhuaChina
  2. 2.Department of PhysicsNanjing UniversityNanjingChina
  3. 3.School of the Gifted YoungUniversity of Science and Technology of ChinaHefeiChina
  4. 4.School of Physical SciencesUniversity of Science and Technology of ChinaHefeiChina

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