• Corpus ID: 117460254

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… 

Figures from this paper

New scale-relativistic derivations of Pauli and Dirac equations

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

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

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

Nonlinear QM as a fractal Brownian motion with complex diffusion constant

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.

Quaternions in mathematical physics (1): Alphabetical bibliography

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 -

Hermann Weyl motivations philosophiques d'un choixMaverik

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

On Nonlinear Quantum Mechanics, Brownian Motion, Weyl Geometry and Fisher Information

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

References

SHOWING 1-5 OF 5 REFERENCES

Fractal Space-Time And Microphysics: Towards A Theory Of Scale Relativity

General introduction from fractal objects to fractal spaces fractal dimension of a quantum path the fractal structure of the quantum space-time towards a linear theory of scale relativity prospects.

Fractal Geometry of Nature

This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.