Note on the geometrical interpretation of quantum groups and noncommutative spaces in gravity

Eugenio Bianchi, Carlo Rovelli

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11 Scopus citations

Abstract

Quantum groups and noncommutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cutoff, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cutoff, where the relevant noncommutative space is the space of directions around any spacetime point. The limitations in angular resolution express the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance 1/√Λ related the cosmological constant Λ. This yields a simple geometrical interpretation for the relation between the quantum deformation parameter q=eiΛlPlanck2 and the cosmological constant, and resolves the difficulty of more conventional interpretations of the physical geometry described by quantum groups or fuzzy spaces.

Original languageEnglish (US)
Article number027502
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume84
Issue number2
DOIs
StatePublished - Jul 20 2011

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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