Loop expansion and the bosonic representation of loop quantum gravity

2016/09/07 by Eugenio Bianchi, Jonathan Guglielmon, Lucas Hackl +1 · 28 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Heat kernel #Hilbert space #Loop (graph theory) #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum gravity #Quantum mechanics #Semiclassical physics #Spin foam #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.94.086009

published in Physical review. D/Physical review. D. 94(8) (American Physical Society) · 33 pages, 2 figures

arxiv created 2016/09/07 · openalex publication_date 2016/10/26 · arxiv updated 2016/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial formalism. The resolution of the identity gives a tool for implementing the projection of states in the full bosonic representation onto the space of solutions to the Gauss and area matching constraints of loop quantum gravity. This procedure is particularly efficient in the semiclassical regime, leading to explicit expressions for the loop expansions of coherent, heat kernel and squeezed states.

Citations

• Spin Networks in Gauge Theory
• Loop space representation of quantum general relativity
• New spinfoam vertex for quantum gravity
• Squeezed vacua in loop quantum gravity
• Space from Hilbert space: Recovering geometry from bulk entanglement
• Gauge-invariant coherent states for loop quantum gravity: II. Non-Abelian gauge groups

Cited by

• Twisted geometries coherent states for loop quantum gravity
• Quantum Geometry of the Light Cone: Fock representation and Spectrum of Radiated Power