Dirac Equation in Scale Relativity
| dc.creator | Celerier, Marie-Noelle | |
| dc.creator | Nottale, Laurent | |
| dc.date | 2001-12-21 | |
| dc.date.accessioned | 2026-07-07T04:12:53Z | |
| dc.date.available | 2026-07-07T04:12:53Z | |
| dc.description | The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The Schrödinger and Klein-Gordon equations have already been demonstrated as geodesic equations in this framework. We propose here a new development of the intrinsic properties of this theory to obtain, using the mathematical tool of Hamilton's bi-quaternions, a derivation of the Dirac equation, which, in standard physics, is merely postulated. The bi-quaternionic nature of the Dirac spinor is obtained by adding to the differential (proper) time symmetry breaking, which yields the complex form of the wave-function in the Schrödinger and Klein-Gordon equations, the breaking of further symmetries, namely, the differential coordinate symmetry ($dx^μ \leftrightarrow - dx^μ$) and the parity and time reversal symmetries. | |
| dc.description | 33 pages, 4 figures, latex. Submitted to Phys. Rev. D | |
| dc.identifier | https://arxiv.org/abs/hep-th/0112213 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0112213 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/51060 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Dirac Equation in Scale Relativity | |
| dc.type | text |