MASSLESS SCALAR FIELD PROPAGATOR IN A QUANTIZED SPACETIME
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Bibliographic record
Abstract
We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H. S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex p 2 plane and goes like 1/p 2 as p 2 →0 from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as p 2 increases to the discretization scale 1/a 2 and remains zero for p 2 >1/a 2 . This behaviour is consistent with the termination of single-particle propagation on the ultraviolet side of the discretization scale. The imaginary part of the propagator, consistent with a multiparticle-state spectral function branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when 1/a 2 <p 2 <∞. The multi-particle aspect of this spectral function within the Källen-Lehmann representation of the propagator leads to the interpretation that the propagation of free-fields in a quantized spacetime is analogous to propagation of interacting fields in a continuous spacetime.
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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 | 0.000 |
| 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)
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 it