$$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ S U ( 3 ) C × S U ( 2 ) L × U ( 1 ) Y × U ( 1 ) X as a symmetry of division algebraic ladder operators
Bibliographic record
Abstract
We demonstrate a model which captures certain attractive features of SU(5) theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras $$\mathbb {R}$$ , $$\mathbb {C}$$ , $$\mathbb {H}$$ , and $$\mathbb {O}$$ . From the SU(n) symmetry of these ladder operators, we then demonstrate a model which has much structural similarity to Georgi and Glashow’s SU(5) grand unified theory. However, in this case, the transitions leading to proton decay are expected to be blocked, given that they coincide with presumably forbidden transformations which would incorrectly mix distinct algebraic actions. As a result, we find that we are left with $$G_{sm} = SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb {Z}_6$$ . Finally, we point out that if U(n) ladder symmetries are used in place of SU(n), it may then be possible to find this same $$G_{sm}=SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb {Z}_6$$ , together with an extra $$U(1)_X$$ symmetry, related to $$B\!-\!L$$ .
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".