Time evolution in a geometric model of a particle
Michael Atiyah, Guido Franchetti, Bernd Schroers
TL;DR
This paper explores a (4+1)-dimensional Ricci-flat spacetime model resembling an evolving Taub-NUT geometry, providing exact solutions to Maxwell and Dirac equations, and relating the model to electron properties and Dirac's Large Number Hypothesis.
Contribution
It introduces a geometric model of a particle based on higher-dimensional spacetime with exact solutions to fundamental equations, linking geometry to particle physics.
Findings
Exact solutions to Maxwell and Dirac equations on the model
Interpretation of solutions as a geometric electron model
Discussion of connections to Dirac's Large Number Hypothesis
Abstract
We analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions in terms of a geometric model of the electron and its spin, and discuss links between the resulting picture and Dirac's Large Number Hypothesis.
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