Related papers: Relativistic SU(4) and Quaternions
In a previous paper [1] we proposed a purely mathematical way to quantum mechanics based on Cartan's simple spinors in their most elementary form of 2 component spinors. Here we proceed along that path proposing, this time, a symmetric…
In this proceeding we summarize results for baryonic contact terms derived within SU(3) chiral effective field theory. The four-baryon contact terms, necessary for the description of the hyperon-nucleon interaction, include SU(3) symmetric…
The structure of spin and isospin is analyzed. Although both spin and isospin are related to the same SU(2) group, they represent different dynamical effects. The Wigner-Racah algebra is used for providing a description of bound states of…
Massless chiral fields of arbitrary spin in six spacetime dimensions, also known as higher spin singletons, admit a simple formulation in terms of $SU^*(4) \cong SL(2,\mathbb{H})$ tensors. We show that, paralleling the four-dimensional…
We associate the lepton-quark families with the vertices of the 4D polytopes 5-cell and the rectified 5-cell derived from the SU(5) Coxeter-Dynkin diagram. The off-diagonal gauge bosons are associated with the root poytope (1000)A4 whose…
Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group we have considered the theory of…
We extend previous work on the IR regime approximation of QCD in which the dominant contribution comes from a dressed two-gluon effective metric-like field $G_{\mu\nu} = g_{ab} B^{a}_{\mu} B^{b}_{\nu}$ ($g_{ab}$ a color SU(3) metric). The…
Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea of…
Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept a similar construction with Dirac spinors. On the other hand, it is…
It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra…
A model in which quarks and leptons consist of three "more elementary" particles of spin 1/2 is proposed. A gauge field theory with SU(4) symmetry that corresponds to this model predicts the existence of two new bosons.
Through the embedding of superconformal quantum mechanics into AdS space, it is possible to construct an effective supersymmetric QCD light-front Hamiltonian for hadrons, which includes a spin-spin interaction between the hadronic…
In part I of [1] we have developed the tensor and spin representation of SO(4) in order to apply it to the simplicial decomposition of the Barrett-Crane model. We attach to each face of a triangle the spherical function constructed from the…
A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over a simple non-division algebra. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the…
Classification of relativistic wave equations is given on the ground of interlocking representations of the Lorentz group. A system of interlocking representations is associated with a system of eigenvector subspaces of the energy operator.…
The Lie algebra su(2) of the classical group SU(2) is built from two commuting quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the…
We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models…
A consistent description of the fundamental interactions of particle physics based upon the assumption of 6 real extra dimensions is presented. The usual 4-dimension space-time, a curved hypersurface with the Lorentz group as local…
The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the vev and the hypercharge splitting (Delta) of right-handed leptons (quarks) in a family vanish and Q=T_0 + Y independently in each helicity sector. As a…
We investigate a model in which spinors are considered as being embedded within the Clifford algebra that operates on them. In Minkowski space $M_{1,3}$, we have four independent 4-component spinors, each living in a different minimal left…