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arXiv · 1408.3260

Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity

Carlo Rovelli
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Abstract

Connes' formula defines a distance in loop quantum gravity, via the spinfoam Dirac operator. A simple notion of spectral distance on a graph can be extended do the discrete Lorentzian context, providing a physically natural example of Lorentzian spectral geometry, with a neat space of Dirac operators. The Hilbert structure of the fermion space is Lorentz covariant rather than invariant.

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Carlo Rovelli. 2014-08-14. Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity. https://arxiv.org/abs/1408.3260

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