Conserved currents of massless fields of spin <i>s</i> ≥ ½
Bibliographic record
Abstract
A complete and explicit classification of all locally constructed conserved currents and underlying conserved tensors is obtained for massless linear symmetric spinor fields of any spin s ≤1/2 in four–dimensional flat spacetime. These results generalize the recent classification in the spin s = 1 case of all conserved currents locally constructed from the electromagnetic spinor field. The present classification yields spin s ≤1/2 analogues of the well–known electromagnetic stress–energy tensor and Lipkin's zilch tensor, as well as a spin s ≤1/2 analogue of a novel chiral tensor found in the spin s = 1 case. The chiral tensor possesses odd parity under a duality symmetry (i.e. a phase rotation) on the spin–s field, in contrast to the even parity of the stress–energy and zilch tensors. As a main result, it is shown that every locally constructed conserved current for each s ≤1/2 is equivalent to a sum of elementary linear conserved currents, quadratic conserved currents associated with the stress–energy, zilch and chiral tensors, and higher–derivative extensions of these currents in which the spin–s field is replaced by its repeated conformally weighted Lie derivatives with respect to conformal Killing vectors of flat spacetime. Moreover, all of the currents have a direct unified characterization in terms of Killing spinors. The cases s = 2, s = 1/2 and s = 3/2 provide a complete set of conserved quantities for propagation of gravitons (i.e. linearized gravity waves), neutrinos and gravitinos, respectively, on flat spacetime. The physical meaning of the zilch and chiral quantities is discussed.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".