Related papers: Knots and Preons
We study 3-dimensional BF theories and define observables related to knots and links. The quantum expectation values of these observables give the coefficients of the Alexander-Conway polynomial.
All known elementary vector particles, the photon, Z, W and the gluons, are described by the gauge theory. They belong to the real representation (1/2,1/2) of the Lorentz group. On the other hand inequivalent representations (1,0) and (0,1)…
We prove that 0 is a characterizing slope for infinitely many knots, namely the genus-1 knots whose knot Floer homology is 2-dimensional in the top Alexander grading, which we classified in recent work and which include all $(-3,3,2n+1)$…
We provide a partial classification of the 3-strand pretzel knots $K = P(p,q,r)$ with unknotting number one. Following the classification by Kobayashi and Scharlemann-Thompson for all parameters odd, we treat the remaining families with $r$…
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…
The electromagnetic form factors of the proton and the neutron are computed within lattice QCD using simulations with quarks masses fixed to their physical values. Both connected and disconnected contributions are computed. We analyze two…
We show that in a self-consistent preon model, where Standard Model quarks and leptons are three-body composites confined at a metacolor scale Lambda_cr ~ 10^14 GeV, both leptoquarks and the Standard Model gauge group SU(3)_c x SU(2)_L x…
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant…
Classical and quantum aspects of noncommutative field theories are discussed. In particular, noncommutative solitons and instantons are constructed and also d=2,3 noncommutative fermion and bosonic (Wess-Zumino-Witten and…
To study symmetry and its breaking in particle physics, plays very important role in order to get useful information about the nature. The classification and arrangements of subatomic particles is also necessary to study particle physics.…
In the present paper a model of preons and their composites is constructed in the framework of the superstring-inspired `flipped' E_6\times \widetilde{E_6} gauge symmetry group which reveals a generalized dual symmetry. Here E_6 and…
If the Lie group of a non-Abelian theory is replaced by the corresponding q-group, one is led to replace the Lie algebra by two dual algebras. The first of these lies close to the Lie algebra that it is replacing while the second introduces…
Jordan, Wigner and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 "ordinary" families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
We study the geometry of interacting knotted solitons. The interaction is local and advances either as a three-body or as a four-body process, depending on the relative orientation and a degeneracy of the solitons involved. The splitting…
A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for…
Families of alternating knots (links) and tangles are studied using as building block the conway defined as the twisting of two strands. The regular representation of knots assumes the projection has the minimal number of overpassings, and…
Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical and mathematical theories. One of the challenging problems in knot theory is distinguishing mutant knots. Mutant…
The structure of the reported excitation spectra of the light unflavored baryons is described in terms of multi-spin valued Lorentz group representations of the so called Rarita-Schwinger (RS) type (K/2, K/2)* [(1/ 2,0)+ (0,1/2)] with…
Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern-Simons theory, these invariants can be found from crossing and braiding matrices of…