Related papers: Braids as a representation space of SU(5)
In this note we study a family of algebras with one parameter defined by generators and relations. The set of generators contains the generators of the usual braids algebra, and another set of generators which is interpreted as ties between…
It is known that the Standard Model describing all of the currently known elementary particles is based on the $U(1)\times SU(2)\times SU(3)$ symmetry. In order to implement this symmetry on the ground of a non-flat space-time manifold one…
Symmetries in the Physical Laws of Nature lead to observable effects. Beyond regularities and conserved magnitudes, the last decades in Particle Physics have seen the identification of symmetries, and their well defined breaking, as the…
Representations of small quantum groups $u_q({\mathfrak{g}})$ at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algebra and mathematical physics. There is an ansatz by Lusztig…
We construct the first three family N=1 supersymmetric string model with Standard Model gauge group SU(3)_C x SU(2)_L x U(1)_Y from an orientifold of type IIA theory on T^6/(Z_2 x Z_2) and D6-branes intersecting at angles. In addition to…
The experimental fact that standard model superpartners have not been observed compels one to consider an alternative implementation for supersymmetry. The basic supermultiplet proposed here consists of a photon and a charged spin 1/2 preon…
Reframing certain well-known particle models in terms of normed division algebras leads to two new results for BSM physics. (1) We identify a sequence of complex structures which induces a cascade of breaking symmetries: Spin(10) $\mapsto$…
Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically…
The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation…
We construct two families of representations of the braid group $B_n$ by considering conjugation actions on congruence subgroups of $GL_{n-1}(Z[t^{\pm 1},q^{\pm 1}])$. We show that many of these representations are faithful modulo the…
A preon-based composite model of the fundamental fermions is discussed, in which the fermions are bound states of smaller entities -- primitive charges (preons). The preon is regarded as a dislocation in a dual 3-dimensional manifold -- a…
Given a hyperplane arrangement in a complex vector space of dimension n, there is a natural associated arrangement of codimension k subspaces in a complex vector space of dimension k*n. Topological invariants of the complement of this…
The loop braid group is the motion group of unknotted oriented circles in $\mathbb{R}^3$. In this paper, we study their representations through the approach inspired by two dimensional topological phases of matter. In principle, the motion…
We start with the consideration of fusion rules of anyonic particles evolving on a 2D surface and the a hypergroup comes with it to construct entangled quantum Markov chains. The fusion rules induce an association scheme with Krein…
The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational…
We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as weighted Lie groupoids. One can think of weighted Lie groupoids as graded manifolds in…
Flat band physics is a central theme in modern condensed matter physics. By constructing a tight--binding single particle system that has vanishing momentum dispersion in one or more bands, and subsequently including more particles and…
Exchanging particles on graphs, or more concretely on networks of quantum wires, has been proposed as a means to perform fault tolerant quantum computation. This was inspired by braiding of anyons in planar systems. However, exchanges on a…
The equations defining pure spinors are interpreted as equations of motion formulated on the lightcone of a ten-dimensional, lorentzian, momentum space. Most of the equations for fermion multiplets, usually adopted by particle physics, are…
An attempt is made to present modern hopes to find manifestation of supersymmetry, a new symmetry that relates bosons and fermions, in particle physics from the point of view of renormalization group flow. The Standard Model of particle…