A connection between spin and statistics based on Galilean invariant delta functions
Bibliographic record
Abstract
We define Galilean invariant delta functions by using the Takahashi formulation, which describes particles with arbitrary spin. The direct calculation of the Galilean invariant delta functions in the (N+1)-dimensional Galilean covariant extended manifolds reveals that, for N odd, there exists a surface on which these delta functions vanish. This feature corresponds to the spacelike separation in the relativistic quantum field theory, and it enables us to discuss a connection between spin and statistics in the Galilean covariant theories. These results show that a spin-statistics connection holds for even-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with odd N≥5. Likewise, we observe that there is no such connection for odd-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with even N≥4. Thus, our results support the claim that there is no connection between spin and statistics in the usual nonrelativistic theory, for which N=4.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".