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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:  https://arxiv.org/abs/2212.12776v2 (pdf) 
Date accepted:  20230811 
Date submitted:  20230208 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 
Specialties: 

Approach:  Theoretical 
Abstract
It is wellknown 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 multiloop multiphoton 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 FeynmanSchwinger parameter space.
Author comments upon resubmission
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 weakfield 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 EulerHeisenberg 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 equalmass case.
Published as SciPost Phys. Proc. 14, 031 (2023)