Comments on my last preprint "Fermions Fields Inside the Geometric Algebra of Spacetime"

I have recently submitted a preprint to HAL (already online) and arxiv (to appear next week). This preprint is humanly written only. It is an incomplete synthesis of six years of hard work. I have had to publish this incomplete version, because of rumors of soon to appear works by AI and human collaborators on similar topics, see here.

 

Even if the paper is humanly written, I have used at several occasion AI tools to

• generate a python code to displays multivectors of the geometric algebra of spacetime in the central notation (bivector isovector products). 
•  generate a generic python code to check the structure constant of SU(3) bivector and isoversor. The code is not specific to Geometric Algebra and was significantly modified afterward.
• check the existing literature 

I have submitted this preprint without checking before its validity with AI tools. I am not confident in AI compagnies: I think the risk is very high that they stole researcher works during their interaction with chat robots. After all, they have already stolen and compressed a huge part of human knowledge inside the internal weights of their models. Actually, learning for a LLM is the modern equivalent of photocopying documents and distributing them instead of their authors (even open licence requires "attribution"). 

I did today an AI check (claude 5.5 analyse) when the preprint appeared on HAL. This rises several good points:

1. There is a sign mistake in Eqs. (271) to (276), easy to spot.
2. The wave equation with strong interaction is not Lorentz covariant: the gauge generators are incompatible with Lorentz transformations (see at the end of this post claude's output). This is easy to see in chiral representation (see Eq. 206 right column). The ℐ3(...)ℐ3B3 operator does not commute with all the generators of isoversor SU(3). It does with the Tμ operators used for the electroweak interaction. In standard representation, operators (…)X and ℐ₂(…)X for arbitrary X indeed commute with left multiplication with a spacetime rotor. This probably let rooms for a color SU(3).
3. The abelian gauge transformation given in Eqs. 212 (left column) and (233) right columns is the Historical one given by D. Hestenes. It is incompatible with the one proposed in the preprint. This is implicit in the preprint, I should have stated it clearly.  

Claude AI suggested other good points on what to do next. Most of those were on my to do list. 

Whenever I have any other corrections, I will post them on this blog (before resubmitting an improved preprint). In any case, I hope this work will foster research at the edge of high energy physics and geometric algebra.

 

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I undertook my PhD research from 2009 to 2012 at the ESPCI (Ecole Supérieur de Physique et Chimie Industrielle), a physics and industrial chemistry school in Paris. I joined the Gulliver Laboratory's department of physico-chemical theory under the supervision of David Lacoste. At that time, I also taught at the Pierre and Marie-Curie University (UPMC) from where I obtained my PhD grant.

For two years, I also worked in Massimiliano Esposito's group on Complex Systems and Statistical Mechanics (the Physics and Material Sciences Research Unit at the University of Luxembourg).

In September of 2014, I took up my current position as a teaching assistant at the University of Orsay (South of Paris), where I work in the statistical physics group of the LPT Orsay (theoretical physics laboratory).






Contact:
Gatien Verley,
Laboratoire de Physique Théorique Orsay,
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Univ. Paris-Sud 11, 91405 Orsay Cedex
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