3d Quantum Gravity: Coarse-Graining and $q$-Deformation
| Autor: | Livine , Etera |
|---|---|
| Přispěvatelé: | École normale supérieure - Lyon ( ENS Lyon ), Institut de Physique Nucléaire de Lyon ( IPNL ), Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Centre National de la Recherche Scientifique ( CNRS ) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
representation: SU(2)
cosmological constant gravitation: model constraint: Hamiltonian deformation Ponzano-Regge model spin: foam [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph] quantization derivative: high triangulation quantum gravity: loop space [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] |
| Zdroj: | Annales Henri Poincare Annales Henri Poincare, 2017, 18 (4), pp.1465-1491. 〈10.1007/s00023-016-0535-0〉 |
| DOI: | 10.1007/s00023-016-0535-0〉 |
| Popis: | International audience; The Ponzano–Regge state-sum model provides a quantization of 3d gravity as a spin foam, providing a quantum amplitude to each 3d triangulation defined in terms of the 6j-symbol (from the spin-recoupling theory of $\mathrm {SU}(2)$ representations). In this context, the invariance of the 6j-symbol under 4-1 Pachner moves, mathematically defined by the Biedenharn–Elliott identity, can be understood as the invariance of the Ponzano–Regge model under coarse-graining or equivalently as the invariance of the amplitudes under the Hamiltonian constraints. Here, we look at length and volume insertions in the Biedenharn–Elliott identity for the 6j-symbol, derived in some sense as higher derivatives of the original formula. This gives the behavior of these geometrical observables under coarse-graining. These new identities turn out to be related to the Biedenharn–Elliott identity for the q-deformed 6j-symbol and highlight that the q-deformation produces a cosmological constant term in the Hamiltonian constraints of 3d quantum gravity. |
| Databáze: | OpenAIRE |
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