Projective Loop Quantum Gravity I. State Space

Understand

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces.

• Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need.
• In [Oko{\l}\'ow 2013, arXiv:1304.6330] the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces.
• The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact).