Construction of Discrete Symmetries Using the Pauli Algebra Form of the Dirac Equation
Bibliographic record
Abstract
Two equations whose variables take values in the Pauli algebra of complex quaternions are shown to be equivalent to the standard Dirac equation and its Hermitian conjugate taken together. They are transformed one into the other by an outer automorphism of the Pauli algebra. Given a solution to the Dirac equation, a new solution is obtained by multiplying it on the right by one of the 16 matrices of the Pauli group. This defines a homomorphism from the Pauli group into the group of discrete symmetries, whose kernel is a cyclic group of order four. The group of discrete symmetries is shown to be the Klein four-group consisting of four elements: the identity Id; the charge conjugation symmetry C; the mass inversion symmetry M; and their composition in either order, CM = MC. The mass inversion symmetry inverts the sign of the mass, leaving the electric charge unchanged. The outer “bar-star” automorphism is identified with the parity operation, resulting in proof of CPT = M or, equivalently, CPTM = Identity.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".