<i>q</i> -deformed 3D loop gravity on the torus
Bibliographic record
Abstract
Abstract The q -deformed loop gravity framework was introduced as a canonical formalism for the Turaev–Viro model (with ), allowing to quantize 3D Euclidean gravity with a (negative) cosmological constant using a quantum deformation of the gauge group. We describe its application to the 2-torus, explicitly writing the q -deformed gauge symmetries and deriving the reduced physical phase space of Dirac observables, which leads back to the Goldman brackets for the moduli space of flat connections. Furthermore it turns out that the q -deformed loop gravity can be derived through a gauge fixing from the Fock–Rosly bracket, which provides an explicit link between loop quantum gravity (for q real) and the combinatorial quantization of 3D gravity as a Chern–Simons theory with non-vanishing cosmological constant . A side-product is the reformulation of the loop quantum gravity phase space for vanishing cosmological constant , based on holonomies and fluxes, in terms of Poincaré holonomies. Although we focus on the case of the torus as an example, our results outline the general equivalence between 3D q -deformed loop quantum gravity and the combinatorial quantization of Chern–Simons theory for arbitrary graph and topology.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".