Infinite Degeneracy of States in Quantum Gravity

TL;DR

This paper demonstrates that in certain quantum gravity models, an infinite variety of conserved quantities exist, which could have significant implications for understanding the fundamental structure of spacetime.

Contribution

It introduces a general result showing infinite conserved quantities in embedded spin-networks within the framework of Braided Ribbon Networks, relevant to Loop Quantum Gravity.

Findings

Infinite conserved quantities exist in embedded spin-networks.

Invariance of conserved quantities in three-valent networks, except in one case.

Implications for the structure of quantum spacetime in Loop Quantum Gravity.

Abstract

The setting of Braided Ribbon Networks is used to present a general result in spin-networks embedded in manifolds: the existence of an infinite number of species of conserved quantities. Restricted to three-valent networks the number of such conserved quantities in a given network is shown to be invariant barring a single case. The implication of these conserved quantities is discussed in the context of Loop Quantum Gravity.