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Group invariants for Feynman diagrams

by Idrish Huet, Michel Rausch de Traubenberg, Christian Schubert

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Michel Rausch de Traubenberg · Christian Schubert
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-08-11
Date submitted: 2023-02-08 13:57
Submitted by: Schubert, Christian
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


It is well-known that the symmetry group of a Feynman diagram can give important information on possible strategies for its evaluation, and the mathematical objects that will be involved. Motivated by ongoing work on multi-loop multi-photon amplitudes in quantum electrodynamics, here I will discuss the usefulness of introducing a polynomial basis of invariants of the symmetry group of a diagram in Feynman-Schwinger parameter space.

Published as SciPost Phys. Proc. 14, 031 (2023)

Author comments upon resubmission

Thank you very much for the report, which we have found very helpful. All sugestions of the report have been taken care of, as will be detailed below.

Christian Schubert (for the authors)

List of changes

1. A paragraph with a short outline of the paper has been added at the end of section 1.
2. At the beginning of section 2, a footnote has been added to explain why we do not consider here the exchange of external lines.
3. The abbreviation EHL is now introduced at the beginning of section 3.
4. The definition of beta_n has been added at the beginning of section 8. At the beginning of section 10, the relation of the oefficients Gamma_n to the weak-field expansion coefficients c_n defined in (4) is now given.
5. What counts here is the total number of Schwinger parameters, that is of internal propagators, and we have now put it like this in the outlook. However, it should be emphasized that the original sentence about many external legs makes sense for the example of the Euler-Heisenberg Lagrangian, since the legs are effectively intergrated out and thus increase the degree of the numerator polynomials rather than the number of Schwinger parameters.
6. All typos have been taken care of - thanks for pointing them out!

Further, a sentence has been added after Fig. 1 to clarify that we have the full permutation symmetry only in the equal-mass case.

Submission & Refereeing History

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Resubmission 2212.12776v2 on 8 February 2023

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