相关论文: Preons, Braid Topology, and Representations of Fun…

We demonstrate a direct correspondence between the basis states of the minimal ideals of the complex Clifford algebras $\mathbb{C}\ell(6)$ and $\mathbb{C}\ell(4)$, shown earlier to transform as a single generation of leptons and quarks…

This paper represents a first attempt at unifying two promising models that attempt to explain the origin of the internal symmetries of leptons and quarks. It is shown that each of the four normed division algebras over the reals admits a…

We describe a simple model, based on the preon model of Shupe and Harari, in which the binding of preons is represented topologically. We then demonstrate a direct correspondence between this model and much of the known phenomenology of the…

The Standard Model of particle physics provides very accurate predictions of phenomena occurring at the sub-atomic level, but the reason for the choice of symmetry group and the large number of particles considered elementary, is still…

In a topological description of elementary matter proposed by Bilson-Thompson, the leptons and quarks of a single generation, together with the electroweak gauge bosons, are represented as elements of the framed braid group of three…

Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…

In this paper we study a Clifford algebra generalization of the quaternions and its relationship with braid group representations related to Majorana fermions. The Fibonacci model for topological quantum computing is based on the fusion…

We study homological representations of mapping class groups, including the braid groups. These arise from the twisted homology of certain configuration spaces, and come in many different flavours. Our goal is to give a unified general…

Some curious structural similarities between a recent braid- and Hurwitz algebraic description of the unbroken internal symmetries for a single generations of Standard Model fermions were recently identified. The non-trivial braid groups…

The Helon model identifies Standard Model quarks and leptons with certain framed braids joined together at both ends by a connecting node (disk). These surfaces with boundary are called braided 3-belts (or simply belts). Twisting and…

In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston's geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement…

We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of the classical braid groups. These representations naturally…

The Standard Model (SM) is a successful approach to particle physics calculations. However, there are indications that the SM is only a good approximation to an underlying non-local reality involving fundamental entities (preons) that are…

For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are…

I report the recent advances in applying (graded) Hopf algebras with braided tensor product in two scenarios: i) paraparticles beyond bosons and fermions living in any space dimensions and transforming under the permutation group; ii)…

Let G be the fundamental group of the complement of a K(G,1) hyperplane arrangement (such as Artin's pure braid group) or more generally a homologically toroidal group (as defined in the paper). The subgroup of elements in the complex…

Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…

We establish counting formulas and bijections for deformations of the braid arrangement. Precisely, we consider real hyperplane arrangements such that all the hyperplanes are of the form $x\_i-x\_j=s$ for some integer $s$. Classical…

It is widely recognized that the main difficulty in designing devices which could process information using quantum states is due to the decoherence of local excitations about a ground state. A solution to this problem was suggested in…

We study the kernels of representations of mapping class groups of surfaces on twisted homologies of configuration spaces. We relate them with the kernel of a natural twisted intersection pairing: if the latter kernel is trivial then the…