On Braid Excitations in Quantum Gravity

Abstract

We propose a new notation for the states in some models of quantum gravity, namely 4-valent spin networks embedded in a topological three manifold. With the help of this notation, equivalence moves, namely translations and rotations, can be defined, which relate the projections of diffeomorphic embeddings of a spin network. Certain types of topological structures, viz 3-strand braids as local excitations of embedded spin networks, are defined and classified by means of the equivalence moves. This paper formulates a mathematical approach to the further research of particle-like excitations in quantum gravity.

24 pages, 16 figures, 5 tables

References in corpus (4)

• Quantum gravity with a positive cosmological constant
• Dual formulation of spin network evolution
• A topological model of composite preons
• Geometry from quantum particles

Cited by in corpus (13)

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• Effective Theory of Braid Excitations of Quantum Geometry in terms of Feynman Diagrams
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• Invariants of Braided Ribbon Networks
• Infinite Degeneracy of States in Quantum Gravity
• Invariants of Spin Networks from Braided Ribbon Networks
• Braided matter interactions in quantum gravity via 1-handle attachment
• Elementary Particles as Gates for Universal Quantum Computation
• Knotted 4-regular graphs: polynomial invariants and the Pachner moves