# Dirac Equation in Scale Relativity

@article{Clrier2001DiracEI, title={Dirac Equation in Scale Relativity}, author={M. N. C{\'e}l{\'e}rier and Laurent Nottale}, journal={arXiv: High Energy Physics - Theory}, year={2001} }

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 Schr\"odinger 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…

## 8 Citations

New scale-relativistic derivations of Pauli and Dirac equations

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In scale relativity, quantum mechanics is recovered by transcribing the classical equations of motion to fractal spaces and demanding, as dictated by the principle of scale relativity, that the form…

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A new nonlinear Schrodinger equation is obtained explicitly from the (fractal) Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy plane-wave solutions…

On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy

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A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space…

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A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the…

Nonlinear QM as a fractal Brownian motion with complex diffusion constant

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A new nonlinear Schrodinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued dif- fusion constant. Real-valued energy (momentum) plane wave…

The physical principles underpinning self-organization in plants.

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Hermann Weyl motivations philosophiques d'un choixMaverik

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1940 fut une année décisive dans le développement intellectuel d’Hermann Weyl (1885-1955), en ce sens qu’elle marque une étape fondamentale dans sa représentation épistémologique de la réalité. En…

Quaternions in mathematical physics (1): Alphabetical bibliography

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This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1 - Alphabetical bibliography, 2 - Analytical bibliography, 3 -…

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