The identification of Young tableaux with angular momentum states
Bibliographic record
Abstract
Young tableaux are used to label the basis vectors of the standard or Young-Yamanouchi basis of the symmetric group. Despite being used for this purpose for some time, a physical interpretation of what they mean has not been given. Weyl tableaux however, which label the basis vectors of the standard or Gelfand basis of the unitary group, do have a physical interpretation. Weyl tableaux correspond to antisymmetrized states with definite total spin, definite spin projection and definite total angular momentum projection. We discuss how a previously well established link between Young and Weyl tableaux may imply Young tableaux are similarly associated with such states. If such an association could be made, calculations using symmetric group bases could be reduced to simple angular momentum manipulations. In particular this would greatly increase the efficiency of calculating the coefficients of fractional parentage of S n , which can in turn be used to calculate unitary recoupling coefficients. We present a methodology for determining whether such an association exists.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".