Bibliographic record
Abstract
A bstract It is known that perturbative expansions in powers of the coupling in quantum mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can be useful at weak coupling but fails at strong coupling. In this work, we present two types of series expansions valid at strong coupling. We apply the series to a basic integral as well as a QM path integral containing a quadratic and quartic term with coupling constant λ . The first series is the usual asymptotic one, where the quartic interaction is expanded in powers of λ . The second series is an expansion of the quadratic part where the interaction is left alone. This yields an absolutely convergent series in inverse powers of λ valid at strong coupling. For the basic integral, we revisit the first series and identify what makes it diverge even though the original integral is finite. We fix the problem and obtain, remarkably, a series in powers of the coupling which is absolutely convergent and valid at strong coupling. We explain how this series avoids Dyson’s argument on convergence. We then consider the QM path integral (discretized with time interval divided into N equal segments). As before, the second series is absolutely convergent and we obtain analytical expressions in inverse powers of λ for the n th order terms by taking functional derivatives of generalized hypergeometric functions. The expressions are functions of N and we work them out explicitly up to third order. The general procedure has been implemented in a Mathematica program that generates the expressions at any order n . We present numerical results at strong coupling for different values of N starting at N = 2. The series matches the exact numerical value for a given N (up to a certain accuracy). The continuum is formally reached when N → ∞ but in practice this can be reached at small N .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".