Automorphisms in Loop Quantum Gravity

Understand

We investigate a certain distributional extension of the group of spatial diffeomorphisms in Loop Quantum Gravity.

• This extension, which is given by the automorphisms Aut(P) of the path groupoid P, was proposed by Velhinho and is inspired by category theory.
• This group is much larger than the group of piecewise analytic diffeomorphisms.
• In particular, we will show that graphs with the same combinatorics but different generalized knotting classes can be mapped into each other.