Bibliographic record
Abstract
In this work, we extend the analysis of the relativistic Dirac–Rosen–Morse problem in curved space–time. For that, we consider the Dirac equation in curved space–time with line element d s2 = (1 + α2 U( r))2(d t2 − d r2) − r2dθ2 − r2sin 2θdϕ2, where α is fine structural constant, U( r) is a scalar potential, and in the presence of the electromagnetic field Aμ = ( V( r), cA( r), 0, 0). Because of the spherical symmetry, the angular spinor is given in terms of the spherical harmonics. For the radial spinor, we apply a unitary transformation and define the vector component of the electromagnetic field A( r) written as a function of V( r) and U( r) so as to solve the radial spinor for Dirac–Rosen–Morse problem. Graphical analyses were performed comparing the eigenenergies and the probability densities in curved and flat space–time to visualize the influence of curvature in space–time on the two-component radial spinor, with the upper and lower components representing the particle and antiparticle, respectively.
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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 | 0.003 |
| 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 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".