2024 - Sustainable Industrial Processing Summit
SIPS 2024 Volume 11. Rowlands Intl. Symp / Mathematics
| Editors: | F. Kongoli, A. Bountis, M. Johnson, S. Karam, L. Kauffman, P. Mandell, M. Mikalajunas, W. Miller, G. Ord, R.M. Santilli, E. Suhir, E. Trell, T. Vougiouklis |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2024 |
| Pages: | 372 pages |
| ISBN: | 978-1-998384-24-2 (CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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TOPOLOGICAL MODELS FOR ELEMENTARY PARTICLES
Louis Kauffman1;1UNIVERSITY OF ILLINOIS AT CHICAGO, Chicago, United States;
Type of Paper: Regular
Id Paper: 310
Topic: 38
Abstract:
In [1] and [2] models of elementary particles are proposed based on combinatorial substructures for quarks.
These papers succeed in given combinatorial models for many particle interactions. In [3] a vector version of the Harari, Shupe models is
given, in which each particle is a four-vector and particle interactions correspond to vector identities. The Lambek model can be matched directly with the Shupe model, but contains
extra information that allows the vectorial work. In [4] a so-called Helon model is given by Bilson-Thompson that uses framed three braids and can be seen as a generalization of the Rishon models of Harari and Schupe. In fact, we find (joint work with David Chester and Xerxes Arsiwalla) that the Lambek model is a nearly perfect intermediary between the Helon model and the Rishon model. There is a direct correspondence between Lambek's four-vectors and the braids in the Helon model, up to a slight readjustment. This means that we are in possession of a dictionary that lets us discuss and compare the structures in these models and to examine possible generalizations of them. We also can use this point of view to see some of the limitations of the Helon model that arise from the non-commutativity of the Artin Braid Group. The talk will present these structures, and our speculations about generalizations and relationships with other topological work such as found in the papers of the author [5], the work of Witten [6] and alternate topological intepretations such as [7], [8], [9] and [10].