Relativistic two-, three- and four-body wave equations in scalar QFT
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Bibliographic record
Abstract
We use the variational method within the Hamiltonian formalism of QFT to derive relativistic two-, three- and four-body wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). The Lagrangian of the theory is reformulated by using Green's functions to express the mediating field in terms of the particle fields. The QFT is then constructed from the resulting reformulated Hamiltonian. Simple Fock-space variational trial states are used to derive relativistic two-, three- and four-body equations. The equations are shown to have the Schrödinger non-relativistic limit, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Ground-state solutions of the relativistic equations are obtained approximately for various strengths of coupling, for both massive and massless mediating fields, and a comparison of the two-, three- and four-particle binding energies is presented.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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