Bilson-Thompson, Sundance; Hackett, Jonathan; Kauffman, Louis; Wan, Yidun Emergent braided matter of quantum geometry. (English) Zbl 1242.83034 SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 014, 43 p. (2012). Summary: We review and present a few new results of the program of emergent matter as braid excitations of quantum geometry that is represented by braided ribbon networks. These networks are a generalisation of the spin networks proposed by Penrose and those in models of background independent quantum gravity theories, such as Loop Quantum Gravity and Spin Foam models. This program has been developed in two parallel but complimentary schemes, namely the trivalent and tetravalent schemes. The former studies the braids on trivalent braided ribbon networks, while the latter investigates the braids on tetravalent braided ribbon networks. Both schemes have been fruitful. The trivalent scheme has been quite successful at establishing a correspondence between braids and Standard Model particles, whereas the tetravalent scheme has naturally substantiated a rich, dynamical theory of interactions and propagation of braids, which is ruled by topological conservation laws. Some recent advances in the program indicate that the two schemes may converge to yield a fundamental theory of matter in quantum spacetime. Cited in 3 Documents MSC: 83C45 Quantization of the gravitational field 83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory 81T99 Quantum field theory; related classical field theories 81V25 Other elementary particle theory in quantum theory 20F36 Braid groups; Artin groups 18D35 Structured objects in a category (MSC2010) 20K45 Topological methods for abelian groups 81P68 Quantum computation Keywords:quantum gravity; loop quantum gravity; spin network; braided ribbon network; emergent matter; braid; standard model; particle physics; unification; braided tensor category; topological quantum computation PDFBibTeX XMLCite \textit{S. Bilson-Thompson} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 014, 43 p. (2012; Zbl 1242.83034) Full Text: DOI arXiv