Related papers: Solitonic Models Based on Quantum Groups and the S…
The aims of this letter are three-fold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the…
The successes and shortcomings of the Standard Model are reviewed, with emphasis on the reasons motivating the need to extend it. The basic elements of grand unification and supersymmetry are described, exploring their phenomenological…
We consider the possibility that the preons defined by the SLq(2) extension of the Standard Model may be identified with Schwinger dyons. The SLq(2) extension is here presented as a model that may exist in either a currently observable…
Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are specific expressions of some q-polynomials as sums of products of q-binomial coefficients. We consider the fermionic formulae associated with general…
We formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible to fulfill the requirements of locality, unitarity and…
This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…
Several refinements are made in a theory which starts with a Planck-scale statistical picture and ends with supersymmetry and a coupling of fundamental fermions and bosons to SO(N) gauge fields. In particular, more satisfactory treatments…
In this work, we attempt to define a notion of compositeness compatible with Quantum Field Theory. Considering the analytic properties of the S-matrix, we conclude that there is no satisfactory definition of compositeness compatible with…
We consider a recent successful model of leptons as Kerr-Newman type Black Holes in a Quantum Mechanical context. The model leads to a cosmology which predicts an ever expanding accelerating universe with decreasing density and to the…
We explore the use of real fermionization as a test case for understanding how specific features of phenomenological interest in the low-energy effective superpotential are realized in exact solutions to heterotic superstring theory. We…
In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories…
We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field…
This paper is a continuation of our works concerning Linear Canonical Transformations (LCT) and Phase Space Representation of Quantum Theory. The purpose is to study the spinorial representation of some particular LCT called Isodispersion…
We have constructed a preonic model starting from a coloured fermionic preon and by postulating a new symmetry, MUSY. This new symmetry is defined via the MU number involving colour, charge and spin properties of the preons. We show that…
We discuss a scenario of ``the path to physics at the Planck scale'' where todays theory of the interactions of elementary particles, the so called Standard Model (SM), emerges as a low energy effective theory describing the long distance…
This survey explores knot polynomials and their categorification, culminating in the homological invariants of knots. We begin with an overview of classical knot polynomials, progressing towards the superpolynomial and its role in unifying…
The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds,…
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
Starting from the existing semiclassical studies on hydrogenoid atoms, we propose a similar intuitive exercise for the three-body quark systems corresponding to protons and neutrons. In the frame of this toy model we try to explain both the…
We consider a composite model in which the standard model fermions are bound states of elementary spin $\frac{1}{2}$ particles, the preons, situated in the conjugate product representation of the color group. In this framework we propose…