The Hamiltonian formulation of N-bein, Einstein-Cartan, gravity in any dimension: the Progress Report (Extended version of a talk given on CAIMS-2009, June 11-14, London, Canada)
Bibliographic record
Abstract
The Hamiltonian formulation of N-bein, Einstein-Cartan, gravity, using its first order form in any dimension higher than two, is analyzed. This Hamiltonian formulation allows to explicitly show where peculiarities of three dimensional case (\textit{A.M.Frolov et al, 0902.0856 [gr-qc]}) occur and make a conjecture, based on presented in this report results, that there is one general for \textit{all} dimensions characteristic of N-bein formulation of gravity: after elimination of second class constraints the algebra of Poisson brackets among remaining first class secondary constraints is the Poincare algebra and in all dimensions N-bein, Cartan-Einstein, gravity \textit{is the Poincare gauge theory}. The gauge symmetry corresponding to the algebra of first class constraints has two parameters - rotational (Lorentz) and translational. Translational invariance is common to all dimensions but some terms in general expressions for gauge transformations of N-beins and connections are zero in a particular, three dimensional, case. The proof of our conjecture is outlined in detail. Some straightforward but tedious calculations remain to be completed to call our conjecture - a theorem and will be reported later.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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".