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Group invariants for Feynman diagrams
by Idrish Huet, Michel Rausch de Traubenberg, Christian Schubert
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Submission summary
| Authors (as registered SciPost users): | Michel Rausch de Traubenberg · Christian Schubert |
| Submission information | |
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| Preprint Link: | scipost_202212_00050v1 (pdf) |
| Date submitted: | 2022-12-18 22:00 |
| 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: |
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Abstract
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.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2022-12-21 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00050v1, delivered 2022-12-21, doi: 10.21468/SciPost.Report.6361
Strengths
1. Compact overview.
2. Well written.
Weaknesses
Slightly too much weight on the example of the Euler-Heisenberg example, while the main topic is the symmetries of Feynman diagrams.
Report
I recommend to publish this article in the proceedings with the minor modifications discussed below.
Requested changes
1. It would be useful to give a brief overview of the paper in section 1, in particular on how the QED example is embedded into the discussion of properties of Feynman integrals and that the author comes back to the latter at the end.
2. In the first sentence of section 2 the symmetries under interchanges of internal lines are emphasized. It would be useful to comment on the exchange symmetries in external lines and why they are not discussed here.
3. At the beginning of section 3 the abbreviation EHL should be introduced, which is used later on page 5.
4. At the beginning of section 8 the beta_n should be defined, i.e. of what are they the coefficients? Similarly for Gamma_n at beginning of section 10.
5. The outlook states that the method of the paper would be useful at large number of external legs. Since it is a symmetry in the internal lines, wouldn't it rather be useful for a large number of internal legs?
6. I found a few typos and similar points:
* Point 3. of Theorem 1: exit[s] and invariant[s]
* Bottom of page 2: This effective Lagrangian hold[s]
* Bottom of page 3: as [a] a tunnelling
* Section 6: Make 2D and $2D$ consistent (text- vs math-mode)
* Bottom of page 6: the z's in the expressions for B,C,G should be in math-mode as on the top of page 7.