Related papers: The SU(3) Algebra in a Cyclic Basis
The Lie algebra of the classical group SU(2) is constructed from two 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 ladder…
In spite of its many successes, the Standard Model makes many empirical assumptions in the Higgs and fermion sectors for which a deeper theoretical basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2) \times su(3)$…
We carry a systematic study of possible models based on the local gauge group SU(3)_c X SU(3)_L X U(1)_X. Old and new models emerge from the analysis.
We construct a class of interacting $(d-2)$-form theories in $d$ dimensions that are `third way' consistent. This refers to the fact that the interaction terms in the $p$-form field equations of motion neither come from the variation of an…
The irreducible representations of the Lie algebra ${\frak su}$(3) describe rotational bands in the context of the nuclear shell and interacting boson models. The density matrices associated with ${\frak su}$(3) provide an alternative…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
By explicit calculation, I determine the structure of the ground ring of the critical $W_3$ gravity and show that there is an $su(3)$ invariant quadratic relation among the six basic elements. By using this result, I also construct some…
Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the…
We investigate self-dualities in three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. The electric and magnetic theories share the same gauge group. The examples include $SU(2N)$, $SO(7)$ and $SO(8)$ with various matter…
$\mathcal{N}=1$ supersymmetric QCD (SQCD) is a possible building block of theories beyond the standard model. It describes the interaction between gluons and quarks with their superpartners, gluinos and squarks. Since supersymmetry is…
In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in R^3 of order less than four are the planes, the spheres and the cylinders. The method used heavily depends on the efficiency of algorithms to compute…
We study the semiclassical asymptotics of twisted algebras induced by symbol correspondences for quark systems ($SU(3)$-symmetric mechanical systems) as defined in our previous paper [3]. The linear span of harmonic functions on (co)adjoint…
Based on local gauge invariance, four different kinds of fundamental interactions in Nature are unified in a theory which has $SU(3)_c \otimes SU(2)_L \otimes U(1) \otimes_s Gravitational Gauge Group$ gauge symmetry. In this approach,…
Pascal routines are provided that generate representations of the group $SU(3)$ and tabulate the Clebsch-Gordan coefficients in the products of representations.
As Lie algebras of compact connected Lie groups, semisimple Lie algebras have wide applications in the description of continuous symmetries of physical systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of generators…
For the SU(3) system of graphs generalizing the ADE Dynkin digrams in the classification of modular invariant partition functions in CFT, we present a general collection of algebraic objects and relations that describe fusion properties and…
In this paper we address the celebrated Albert problem for exceptional Jordan algebras (i.e. Albert algebras): Does every Albert division algebra contain a cubic cyclic subfield? We prove that for any Albert division algebra $A$ over a…
A scheme to perform the Cartan decomposition for the Lie algebra su(N) of arbitrary finite dimensions is introduced. The schme is based on two algebraic structures, the conjugate partition and the quotient algebra, that are easily generated…
We prove that for all natural numbers $m$ and $k$ where $k$ is odd, there exists a natural number $N(k)$ such that any 3-connected cubic graph with at least $N(k)$ vertices contains a cycle of length $m$ modulo $k$. We also construct a…
Monopoles are solutions of an SU(2) gauge theory in $\mathbb{R}^{3}$ satisfying a lower bound for energy and certain asymptotic conditions, which translate as topological properties encoded in their charge. Using methods from integrable…