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 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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".