Asymptotic freedom and quarks confinement treated through Thompson’s approach
Bibliographic record
Abstract
In this work, we first use Thompson’s renormalization group method to treat QCD–vacuum behavior close to the regime of asymptotic freedom. The QCD–vacuum behaves effectively like a “paramagnetic system” of a classical theory in the sense that virtual color charges (gluons) emerge in it as a spin effect of a paramagnetic material when a magnetic field aligns their microscopic magnetic dipoles. Making a classical analogy with the paramagnetism of Landau’s theory, we are able to introduce a kind of Landau effective action without temperature and phase transition for just representing QCD–vacuum behavior at higher energies as being magnetization of a paramagnetic material in the presence of a magnetic field H. This reasoning allows us to use Thompson’s heuristic approach to obtain an “effective susceptibility” (χ > 0) of the QCD–vacuum. It depends on the logarithm of the energy scale u to investigate hadronic matter. Consequently, we are able to get an “effective magnetic permeability” (μ > 1) of such a “paramagnetic vacuum”. As the QCD–vacuum must obey Lorentz invariance, the attainment of μ > 1 must simply require that the “effective electrical permittivity” is ϵ < 1 in such a way that μϵ = 1 (c2 = 1). This leads to the anti-screening effect, where the asymptotic freedom takes place. On the other hand, quarks confinement, a subject which is not treatable by perturbative calculations, is worked by the present approach. We apply the method to study this issue for obtaining the string constant, which is in agreement with the experiments.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".