Loop gravity in terms of spinors

Abstract

We show that loop gravity can equally well be formulated in in terms of spinorial variables (instead of the group variables which are commonly used), which have recently been shown to provide a direct link between spin network states and discrete geometries. This results in a new, unitarily equivalent formulation of the theory on a generalized Bargmann space. Since integrals over the group are exchanged for straightforward integrals over the complex plane we expect this formalism to be useful to efficiently organize practical calculations.

4 pages, based on a talk given at Loops '11, Madrid, to appear in Journal of Physics: Conference Series (JPCS)

References in corpus (5)

• Polyhedra in loop quantum gravity
• From twistors to twisted geometries
• U(N) tools for Loop Quantum Gravity: The Return of the Spinor
• Dynamics for a 2-vertex Quantum Gravity Model
• Revisiting the Simplicity Constraints and Coherent Intertwiners

Cited by in corpus (13)

• Deformation Operators of Spin Networks and Coarse-Graining
• Deformations of Polyhedra and Polygons by the Unitary Group
• From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
• A new Hamiltonian for the Topological BF phase with spinor networks
• Holonomy Operator and Quantization Ambiguities on Spinor Space
• Loop expansion and the bosonic representation of loop quantum gravity
• Bubble Networks: Framed Discrete Geometry for Quantum Gravity
• Spinors and Twistors in Loop Gravity and Spin Foams
• The Construction of Spin Foam Vertex Amplitudes
• Local Observables in ${\mathrm{SU}}_q(2)$ Lattice Gauge Theory
• Polyhedron phase space using 2-groups: kappa-Poincare as a Poisson 2-group
• New insights in quantum geometry
• Nonlocal correlations for semiclassical states in loop quantum gravity