PECULIARITIES OF THE CANONICAL ANALYSIS OF THE TWO-DIMENSIONAL FIRST-ORDER EINSTEIN–HILBERT ACTION IN TERMS OF THE METRIC TENSOR OR THE METRIC DENSITY
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Bibliographic record
Abstract
The peculiarities of doing a canonical analysis of the first-order formulation of the Einstein–Hilbert action in terms of either the metric tensor g αβ or the metric density [Formula: see text] along with the affine connection are discussed. It is shown that the difference between using g αβ as opposed to h αβ appears only in two spacetime dimensions. Despite there being a different number of constraints in these two approaches, both formulations result in there being a local Poisson brackets algebra of constraints with field independent structure constants, closed off-shell generators of gauge transformations and off-shell invariance of the action. The formulation in terms of the metric tensor is analyzed in detail and compared with earlier results obtained using the metric density. The gauge transformations, obtained from the full set of first-class constraints, are different from a diffeomorphism transformation in both cases.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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