Quantum particles in noncommutative spacetime: An identity crisis
Bibliographic record
Abstract
We argue that the notion of identical particles is no longer well defined in quantum systems governed by noncommutative deformations of spacetime symmetries. Such models are characterized by four-momentum space given by a non-Abelian Lie group. Our analysis is based on the observation that, for states containing more than one particle, only the total momentum of the system is a well-defined quantum number. Such total momentum is obtained from the non-Abelian composition of the particles individual momenta which are no longer uniquely defined. The main upshot of our analysis is that all previous attempts to construct Fock spaces for these models rested on wrong assumptions and indeed have been unsuccessful. We also show how the natural braiding of momentum quantum numbers which characterizes the exchange of factors in the tensor product of states is covariant under relativistic transformations, thus solving a long-standing problem in the field.
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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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.013 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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".