Dirac Equation in Scale Relativity
Abstract
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 nondifferentiable (fractal) spacetime. The Schrödinger and KleinGordon 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 biquaternions, a derivation of the Dirac equation, which, in standard physics, is merely postulated. The biquaternionic nature of the Dirac spinor is obtained by adding to the differential (proper) time symmetry breaking, which yields the complex form of the wavefunction in the Schrödinger and KleinGordon equations, the breaking of further symmetries, namely, the differential coordinate symmetry ($dx^{\mu} \leftrightarrow  dx^{\mu}$) and the parity and time reversal symmetries.
 Publication:

arXiv eprints
 Pub Date:
 December 2001
 arXiv:
 arXiv:hepth/0112213
 Bibcode:
 2001hep.th...12213C
 Keywords:

 High Energy Physics  Theory
 EPrint:
 33 pages, 4 figures, latex. Submitted to Phys. Rev. D