Notes on a few quasilocal properties of Yang-Mills theory
Bibliographic record
Abstract
Gauge theories possess non-local features that, in the presence of boundaries, inevitably lead to subtleties. In this article, we continue our study of a unified solution based on a geometric tool operating on field-space: a connection form. We specialize to the $D+1$ formulation of Yang-Mills theories on configuration space, and we precisely characterize the gluing of the Yang-Mills field across regions. In the $D+1$ formalism, the connection-form splits the electric degrees of freedom into their pure-radiative and Coulombic components, rendering the latter as conjugate to the pure-gauge part of the gauge potential. Regarding gluing, we obtain a characterization for topologically simple regions through closed formulas. These formulas exploit the properties of a generalized Dirichlet-to-Neumann operator defined at the gluing surface; through them, we find only the radiative components and the local charges are relevant for gluing. Finally, we study the gluing into topologically non-trivial regions in 1+1 dimensions. We find that in this case, the regional radiative modes do not fully determine the global radiative mode (Aharonov-Bohm phases). For the global mode takes a new contribution from the kernel of the gluing formula, a kernel which is associated to non-trivial cohomological cycles. In no circumstances do we find a need for postulating new local degrees of freedom at boundaries. $\text{The partial results of these notes have been completed and substantially clarified in a more recent, comprehensive article from October 2019. (titled: "The quasilocal degrees of freedom of Yang-Mills theory").}$
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".