Emergent Braided Matter of Quantum Geometry

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2012
• Main Authors: Bilson-Thompson, S., Hackett, J., Kauffman, L., Wan, Y.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148393
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Emergent Braided Matter of Quantum Geometry / S. Bilson-Thompson, J. Hackett, L. Kauffman, Y. Wan // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 106 назв. — англ.

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.