SciPost Submission Page
On Old Relations of Lie Theory, Classical Geometry and Gauge Theory
by Rolf Dahm
Submission summary
| Authors (as registered SciPost users): | Rolf Dahm |
| Submission information | |
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| Preprint Link: | scipost_202212_00049v1 (pdf) |
| Date accepted: | Aug. 11, 2023 |
| Date submitted: | Dec. 18, 2022, 9:56 p.m. |
| Submitted by: | Rolf Dahm |
| 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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| Approaches: | Theoretical, Phenomenological |
Abstract
Having been led by hadron interactions and low-energy photoproduction to SU(4) and non-compact SU$*$(4) symmetry, the general background turned out to be projective geometry (PG) of $P^3$, or when considering line and Complex geometry to include gauge theory, aspects of $P^5$. Point calculus and its dual completion by planes introduced quaternary (quadratic) 'invariants' $x_{\mu}x^{\mu}=0$ and $p_{\mu}p^{\mu}=0$, and put focus on the intermediary form $(xu)$ and its treatment. Here, the major result is the identification of the symmetric {\bf{\underline{20}}} of SU(4) comprising nucleon and Delta states as related to the quaternary cubic forms discussed by Hilbert in his work on full invariant systems. So PG determines {\it geometrically} the scene by representations (reps) and invariant theory without having to force affine restrictions and additional (spinorial or gauge) rep theory.
Current status:
Editorial decision:
For Journal SciPost Physics Proceedings: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2023-1-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00049v1, delivered 2023-01-29, doi: 10.21468/SciPost.Report.6629
Strengths
Weaknesses
Report
An interesting paper that shows that among the original approach to Lie groups, there remain a number of questions that are still of interest for physical applications.