Loop expansion and the bosonic representation of loop quantum gravity
arXiv:1609.02219 · doi:10.1103/PhysRevD.94.086009
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.
33 pages, 2 figures
References in corpus (7)
- A new spinfoam vertex for quantum gravity
- Polyhedra in loop quantum gravity
- U(N) tools for Loop Quantum Gravity: The Return of the Spinor
- Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
- Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
- Spinfoams in the holomorphic representation
- Revisiting the Simplicity Constraints and Coherent Intertwiners