Gauge Symmetry Breaking Lattice Regularizations and their Continuum Limit
Bibliographic record
Abstract
Lattice regularizations are pivotal in the non-perturbative quantization of gauge field theories. Wilson's proposal to employ group-valued link fields simplifies the regularization of gauge fields in principal fiber bundles, preserving gauge symmetry within the discretized lattice theory. Maintaining gauge symmetry is desirable as its violation can introduce unwanted degrees of freedom. However, not all theories with gauge symmetries admit gauge-invariant lattice regularizations, as observed in general relativity where the diffeomorphism group serves as the gauge symmetry. In such cases, gauge symmetry-breaking regularizations become necessary. In this paper, we argue that a broken lattice gauge symmetry is acceptable as long as gauge symmetry is restored in the continuum limit. We propose a method to construct the continuum limit for a class of lattice-regularized Hamiltonian field theories, where the regularization breaks the Lie algebra of first-class constraints. Additionally, we offer an approach to represent the exact gauge group on the Hilbert space of the continuum theory. The considered class of theories is limited to those with first-class constraints linear in momenta, excluding the entire gauge group of general relativity but encompassing its subgroup of spatial diffeomorphisms. We discuss potential techniques for extending this quantization to the full gauge group.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".