Two-Component Formulation of the Wheeler-DeWitt Equation,” Uni. of Alberta preprint no
Bibliographic record
Abstract
The Wheeler-DeWitt equation for the minimally coupled FRW-massive-scalar-field minisuperspace is written as a two-component Schrödinger equation with an explicitly ‘time’-dependent Hamiltonian. This reduces the solution of the Wheeler-DeWitt equation to the eigenvalue problem for a non-relativistic one-dimensional harmonic oscillator and a series of trivial algebraic equations whose inductive solution may be easily found. In particular, it is shown that there is a simple double grading of the solutions of the Wheeler-DeWitt equation which determines two classes of definite-parity solutions. A detailed analysis of these solutions is performed. Since every solution may be written as the superposition (sum) of the definite-parity solutions, the analysis of the latter yields the structure of the general solutions. Furthermore, it is shown that real solutions such as that of Hartle and Hawking have definite parity. The results of this article are independent of the choice of the inner product on the space of solutions and boundary conditions.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".