SPECTRUM AND WAVE FUNCTIONS OF U(1)<sub>2+1</sub> LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN
Bibliographic record
Abstract
We address an old problem in lattice gauge theory — the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. Using the method of Monte Carlo with importance sampling, we construct a stochastic basis of Bargmann link states, drawn from a physical probability density function. In the next step, we compute transition amplitudes between stochastic basis states. Then, we extract energy spectra and wave functions from a matrix of transition elements. To test this method, we apply it to U(1) lattice gauge theory in (2+1) dimensions and compute the energy spectrum, wave functions and thermodynamic functions of the electric Hamiltonian of this theory. We compare the numerical results with the analytical results and observe a reasonable scaling of energies and wave functions in the variable of time.
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How this classification was reachedexpand
Full frame distilled prediction
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 | 0.000 |
| 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 |
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 teacher head, 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".