Lorentz Invariance of the Multidimensional Dirac-Hestenes Equation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909972421410816 |
|---|---|
| author | Rumyantseva, S. V. Shirokov, D. S. |
| author_facet | Rumyantseva, S. V. Shirokov, D. S. |
| contents | This paper investigates the Lorentz invariance of the multidimensional Dirac-Hestenes equation, that is, whether the equation remains form-invariant under pseudo-orthogonal transformations of the coordinates. We examine two distinct approaches: the tensor formulation and the spinor formulation. We first present a detailed examination of the four-dimensional Dirac-Hestenes equation, comparing both transformation approaches. These results are subsequently generalized to the multidimensional case with (1,n) signature. The tensor approach requires explicit invariants, while the spinor formulation naturally maintains Lorentz covariance through spin group action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lorentz Invariance of the Multidimensional Dirac-Hestenes Equation Rumyantseva, S. V. Shirokov, D. S. Mathematical Physics 35Q41, 81Q05, 15A66, 70S15, 81T13 This paper investigates the Lorentz invariance of the multidimensional Dirac-Hestenes equation, that is, whether the equation remains form-invariant under pseudo-orthogonal transformations of the coordinates. We examine two distinct approaches: the tensor formulation and the spinor formulation. We first present a detailed examination of the four-dimensional Dirac-Hestenes equation, comparing both transformation approaches. These results are subsequently generalized to the multidimensional case with (1,n) signature. The tensor approach requires explicit invariants, while the spinor formulation naturally maintains Lorentz covariance through spin group action. |
| title | Lorentz Invariance of the Multidimensional Dirac-Hestenes Equation |
| topic | Mathematical Physics 35Q41, 81Q05, 15A66, 70S15, 81T13 |
| url | https://arxiv.org/abs/2512.18347 |