English

Feynman integral relations from parametric annihilators

High Energy Physics - Theory 2019-02-14 v2 Mathematical Physics math.MP

Abstract

We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of Loeser and Sabbah, we conclude that the number of master integrals is computed by the Euler characteristic of the Lee-Pomeransky polynomial. We illustrate techniques to compute this Euler characteristic in various examples and compare it with numbers of master integrals obtained in previous works.

Keywords

Cite

@article{arxiv.1712.09215,
  title  = {Feynman integral relations from parametric annihilators},
  author = {Thomas Bitoun and Christian Bogner and Rene Pascal Klausen and Erik Panzer},
  journal= {arXiv preprint arXiv:1712.09215},
  year   = {2019}
}

Comments

v2: new section 3.1 added, several misprints corrected and additional remarks

R2 v1 2026-06-22T23:29:10.583Z