Automorphisms in Loop Quantum Gravity

Abstract

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. We describe the automorphism-invariant Hilbert space and comment on how a combinatorial formulation of LQG might arise.

57 pages, 7 figures

References in corpus (6)

• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Parallel Transport and Functors
• Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Exploring the diffeomorphism invariant Hilbert space of a scalar field
• Construction of Generalized Connections

Cited by in corpus (8)

• Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
• Fisher Metric, Geometric Entanglement and Spin Networks
• Structural aspects of loop quantum gravity and loop quantum cosmology from an algebraic perspective
• Symmetry restriction and its application to gravity
• Cosmological states in loop quantum gravity on homogeneous graphs
• The Spacetime Picture in Quantum Gravity
• The Dirac Sea for the Non-Separable Hilbert Spaces
• Groups of generalized flux transformations in the space of generalized connections