Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators

Understand

In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored.

• After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert space, on which the imposition of different forms of the simplicity constraints can be studied.
• We detail under which conditions this Hilbert space can be mapped to a Hilbert space of projected spin networks or an ordinary spin network space.
• These considerations allow to derive the general form of the transfer operators which generates discrete time evolution.