Twistors to twisted geometries

2010/06/01 by Laurent Freidel, Simone Speziale · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Combinatorics #Computer science #Cosmology and Gravitation Theories #Geometry #Graph #Interpretation (philosophy) #Loop (graph theory) #Mathematics #Noncommutative and Quantum Gravity Theories #Phase space #Physics #Pure mathematics #Quantum mechanics #Space (punctuation) #Theoretical physics #Topology (electrical circuits) #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.82.084041

published as Phys.Rev.D82:084041,2010 · 9 pages

arxiv created 2010/06/01 · openalex publication_date 2010/10/25 · arxiv updated 2010/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition dual to the graph. Here we unravel the origin of the phase space from a geometric interpretation of twistors.

Citations

• The symplectic geometry of polygons in Euclidean space
• Geometric quantization and multiplicities of group representations
• Triangulated surfaces in twistor space: a kinematical set up for open/closed string duality

Cited by

• Twistorial structure of loop-gravity transition amplitudes
• Spinning geometry = Twisted geometry
• Squeezed vacua in loop quantum gravity
• Loop quantum gravity [wikipedia]