Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity

2014/08/14 by Carlo Rovelli, Rovelli, Carlo
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1408.3260

openalex publication_date 2014/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Equivariant Lorentzian Spectral Triples

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