The Koslowski- Sahlmann representation: Gauge and diffeomorphism invariance

Understand

The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere.

• This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity.
• Koslowski generalised the LQG representation so as to describe states labelled by smooth non- degenerate triad fields.
• His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods.