Large<i>N</i>dynamics in QED in a magnetic field
Bibliographic record
Abstract
The expression for the dynamical mass of fermions in QED in a magnetic field is obtained for a large number of the fermion flavor N in the framework of $1/N$ expansion. The existence of a threshold value ${N}_{\mathrm{thr}},$ dividing the theories with essentially different dynamics, is established. For the number of flavors $N\ensuremath{\ll}{N}_{\mathrm{thr}},$ the dynamical mass is very sensitive to the value of the coupling constant ${\ensuremath{\alpha}}_{b},$ related to the magnetic scale $\ensuremath{\mu}=\sqrt{|\mathrm{eB}|}.$ For N of the order of ${N}_{\mathrm{thr}}$ or larger, a dynamics similar to that in the Nambu--Jona-Lasinio model with a cutoff of the order of $\sqrt{|\mathrm{eB}|}$ and the dimensional coupling constant $G\ensuremath{\sim}1/(N|\mathrm{eB}|)$ takes place. In this case, the value of the dynamical mass is essentially ${\ensuremath{\alpha}}_{b}$ independent (the dynamics with an infrared stable fixed point). The value of ${N}_{\mathrm{thr}}$ separates a weak coupling dynamics (with ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\alpha}}}_{b}\ensuremath{\equiv}N{\ensuremath{\alpha}}_{b}\ensuremath{\ll}1)$ from a strong coupling one (with ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\alpha}}}_{b}\ensuremath{\gtrsim}1)$ and is of the order of $1/{\ensuremath{\alpha}}_{b}.$
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| 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".