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arXiv · 0902.0143

On the Ricci flow and emergent quantum mechanics

J. M. Isidro·J. L. G. Santander·P. Fernandez de Cordoba
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Abstract

The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential function that is proportional to the Ricci scalar curvature of configuration space. This allows one to obtain Schroedinger quantum mechanics from Perelman's action functional: the quantum-mechanical wavefunction is the exponential of $i$ times the conformal factor of the metric on configuration space. We explore links with the recently discussed emergent quantum mechanics.

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J. M. Isidro, J. L. G. Santander, P. Fernandez de Cordoba. 2009-02-01. On the Ricci flow and emergent quantum mechanics. https://doi.org/10.1088/1742-6596/174/1/012033

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