Matching Lagrangian and Hamiltonian simulations in (2+1)-dimensional U(1) gauge theory
Bibliographic record
Abstract
Abstract At finite lattice spacing, Lagrangian and Hamiltonian predictions differ due to discretization effects. In the Hamiltonian limit, i.e. at vanishing temporal lattice spacing $$a_t$$ a t , the path integral approach in the Lagrangian formalism reproduces the results of the Hamiltonian theory. In this work, we numerically calculate the Hamiltonian limit of a U (1) gauge theory in $$(2+1)$$ ( 2 + 1 ) dimensions. This is achieved by Monte Carlo simulations in the Lagrangian formalism with lattices that are anisotropic in the time direction. For each ensemble, we determine the ratio between the temporal and spatial scale with the static quark potential and extrapolate to $$a_t \rightarrow 0$$ a t → 0 . Our results are compared with the data from Hamiltonian simulations at small volumes, showing agreement within $$<2\sigma $$ < 2 σ . These results can be used to match the two formalisms.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".