Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity

Carlo Rovelli 1, 2
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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https://hal.archives-ouvertes.fr/hal-01476566
Contributor : Carlo Rovelli <>
Submitted on : Saturday, February 25, 2017 - 12:04:33 AM
Last modification on : Thursday, March 15, 2018 - 4:56:08 PM

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  • HAL Id : hal-01476566, version 1
  • ARXIV : 1408.3260

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Carlo Rovelli. Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity. 2014. ⟨hal-01476566⟩

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