Related papers: Knots and Preons
The refined Chern-Simons theory is a one-parameter deformation of the ordinary Chern-Simons theory on Seifert manifolds. It is defined via an index of the theory on N M5 branes, where the corresponding one-parameter deformation is a natural…
We present a first-principles derivation of the masses of all twelve known fermions -- three charged leptons, six quarks, and three neutrinos -- and the fine-structure constant $\alpha^{-1}$, from a single discrete functional equation, the…
The electroproduction of kaon on proton has been studied using two covariant isobar models. The models incorporate propagators and vertex factors developed in our previous works. In total, the current study includes 26 nucleon resonances…
The standard forms of supersymmetry and supergravity are inextricably wedded to Lorentz invariance. Here a Lorentz-violating form of supergravity is proposed. The superpartners have exotic properties that are not possible in a theory with…
It is conjectured that all known fermions are topological solitons. This could explain the non-observation of bosonic leptons and baryons and provide a physical mechanism for the Pauli exclusion principle.
I discuss in detail the construction of realistic superstring standard--like models in the four dimensional free fermionic formulation. The analysis results in a restricted class of models with unique characteristics: (i) Three and only…
One of the interesting features in unification models and supersymmetric unification models is that the chiral states of quarks and leptons in a family including a right-handed neutrino can be fitted neatly into a fundamental spinor…
In 2000, Thomas Fink and Young Mao studied neck ties and, with certain assumptions, found 85 different ways to tie a neck tie. They gave a formal language which describes how a tie is made, giving a sequence of moves for each neck tie. The…
The fermionic fields of one generation of the Standard Model, including the Lorentz spinor degrees of freedom, can be identified with components of a single real 64-dimensional semi-spinor representation S of the group Spin(11,3). We…
We define a knot invariant and a 2-knot invariant from any finite categorical group. We calculate an explicit example for the Spun Trefoil.
Spinor structure is understood as a totality of tensor products of biquaternion algebras, and the each tensor product is associated with an irreducible representation of the Lorentz group. A so-defined algebraic structure allows one to…
We present a study on ab-initio calculations of three-neutron correlators from Lattice QCD. We extend the method of baryon blocks to systems of three spacially displaced baryons. This allows the measurement of three-neutron $p$-wave…
A well pronounced spin--grouping of baryon resonances to O(4) partial waves is found in baryon spectra and shown to be well interpreted in terms of Lorentz group representations of the type (1/2 +l', 1/2 +l')* [(1/2, 0)+(0,1/2)] with l'…
We study multipole decompositions of the electromagnetic currents of spin-1/2, 1, and 3/2 particles described in terms of Lagrangians designed to reproduce representation specific wave equations which are second order in the momenta and…
A realistic extension of the minimal $SU(5)$ theory consisting of the addition of an adjoint fermion is known to predict light real fermion and scalar weak triplets, potentially accessible at the LHC. These particles, in addition to playing…
Knots have been considered to be useful models for simulating molecular chains such as DNA and proteins. One quantity that we are interested on molecular knots is the minimum number of monomers necessary to realize a knot. In this paper we…
We classify elementary particles according to their behaviour under the action of the full inhomogeneous Lorentz group. For fundamental fermions, this approach leads us to delineate fermions into eight basic families or `types',…
We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured…
Let $\Gamma$ be the fundamental group of the exterior of a knot in the three-sphere. We study deformations of representations of $\Gamma$ into $\mathrm{SL}_n(\mathbf{C})$ which are the sum of two irreducible representations. For such…
This is an extension of quantum spinor construction in \cite{DF2}. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum spinor representations of $U_q(\hat{\frak…