Conserved Quantities and the Algebra of Braid Excitations in Quantum Gravity

TL;DR

This paper explores how braid-like excitations in quantum gravity exhibit conservation laws and form a noncommutative algebra, revealing new algebraic structures in the context of embedded spin networks.

Contribution

It introduces the derivation of conservation laws and the algebraic structure of braid excitations in quantum gravity, highlighting the role of actively-interacting braids.

Findings

Conservation laws are derived from braid interactions.

Stable braid excitations form a noncommutative algebra.

Actively-interacting braids constitute a subalgebra.

Abstract

We derive conservation laws from interactions of braid-like excitations of embedded framed spin networks in Quantum Gravity. We also demonstrate that the set of stable braid-like excitations form a noncommutative algebra under braid interaction, in which the set of actively-interacting braids is a subalgebra.