Related papers: Relativistic SU(4) and Quaternions
We examine nucleon-nucleon realistic interactions, based on their SU(3) decomposition to SU(3)-symmetric components. We find that many of these interaction components are negligible, which, in turn, allows us to identify a subset of…
Starting from ${\cal N}=4$ SYM and using an appropriate Higgs mechanism we reconsider the construction of a scalar field theory non-minimally coupled to a Coulomb potential with a relativistic SO(4) symmetry and check for scalar field…
We present a study of spectroscopy of SU(4) lattice gauge theory coupled to two flavors of Dirac fermions in the anti-symmetric two index representation. The fermion representation is real, and the pattern of chiral symmetry breaking is…
We investigate quantum deformation of conformal algebras by constructing the quantum space for $sl_q(4,C)$. The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformed $su(4)$ and…
Effect of quantum fluctuations concerned with the orbital degrees of freedom is discussed for the model with SU(4) symmetry in one dimension. An effective Hamiltonian is derived from the orbitally degenerate Hubbard model at quarter…
The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.
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.…
We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
Attention is focused on q-deformed quantum algebras with physical importance, i.e. $U_{q}(su_{2})$, $U_{q}(so_{4})$ and q-deformed Lorentz algebra. The main concern of this article is to assemble important ideas about these symmetry…
Different ways of representing the group $SU(3)$ within a Geometric Algebra approach are explored. As part of this we consider characteristic multivectors for $SU(3)$, and how these are linked with decomposition of generators into commuting…
We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1/2 states, then the same…
It is shown that quarks and leptons can couple intrinsically to pure supergravity, preserving for this context the degeneracy of globally supersymmetric vacua, and specifically preserving the vacuum that is characterized by SU(4)XU(1). A…
This paper is a PhD thesis defended at Institute of Theoretical Physics and Astronomy on 18 December, 1998. The following (abbreviated) statements represent the main results of the work: 1.Each of SU(2) representation j yields the different…
Tensor, matrix and quaternion formulations of Dirac-K\"ahler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The…
In this thesis, we develop techniques for the analysis of SO(2N) invariant couplings which allows a full exhibition of the SU(N) invariant content of the spinor and tensor representations. The techniques utilize a so called Basic Theorem…
We assemble the spectrum of single-trace operators in free N=4 SU(N) SYM theory into irreducible representations of the Higher Spin symmetry algebra hs(2,2|4). Higher Spin representations or YT-pletons are associated to Young tableaux (YT)…
Tensor products of standard model bosons and fermions form a spin-2 self-realization of SU(5), and because every quark can be interpreted as a lepton that has coupled to an appropriate element of this adjoint representation, and inversely,…
The "spin-up" and "spin-down" projections of the second order, chiral form of Dirac Theory are shown to fit a superposition of forms predicted in an earlier classical, complex scalar gauge theory (April, 1992 Class. Quantum Grav.). In some…
We propose a formal framework for a noncommutative Kadomtsev--Petviashvili (KP) hierarchy which is covariant under the action of $SU(3)$ and compatible with a Lorentzian structure encoded in a twisted quaternionic (or Clifford) algebra. The…