Related papers: The SU(3) Algebra in a Cyclic Basis
All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi. In terms of a suitable basis of 1-forms the commutation relations can be expressed with…
A noncommutative *-algebra that generalizes the canonical commutation relations and that is covariant under the quantum groups SOq(3) or SOq(1,3) is introduced. The generating elements of this algebra are hermitean and can be identified…
We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above…
A generalization of the term "generalized Clifford algebras" (as appears in papers on advances in applied Clifford algebras) is introduced. This algebra is studied by means of structure theory of central simple algebras. A graph theoretical…
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…
The work is a brief review of the theory based on the $SU(3)_c \otimes SU(3)_L \otimes U(1)_X$ gauge group in the presence of Heavy Leptons. Recent analysis have established a set of four possible variants for the 3-3-1HL, whose content…
We study the $\eta$NN coupling constant using the method of QCD sum rules starting from the vacuum-to-eta correlation function of the interpolating fields of two nucleons. The matrix element of this correlation has been taken with respect…
We construct the nonlinear $W(sl(N+3),sl(3))$ algebras and find the spectrum of values of the central charge that gives rise, by contracting the $W(sl(N+3),sl(3))$ algebras, to a $W_3$ algebra belonging to the coset…
Three-quark nucleon interpolating fields in QCD have well-defined SU_L(3)*SU_R(3) and U_A(1) chiral transformation properties, viz. [(6,3)+(3,6)], [(3,3_bar)+(3_bar,3)], [(8,1)+(1,8)] and their "mirror" images, Ref.[9]. It has been shown…
We analyze two recent models based on the gauge group SU(3)$_c\times$SU(3)$_L\times$U(1)$_N$ where each generation is not anomaly-free, but anomaly cancels when three generations are taken into account. We show that the most general Yukawa…
We calculate the vacuum stability conditions and renormalisation group equations for the extensions of standard model with a higher colour multiplet scalar up to the representation $\mathbf{15'}$ that leaves the strong interaction…
We construct the nonlinear $N=2$ super-$W_3^{(2)}$ algebra with an arbitrary central charge at the classical level in the framework of Polyakov "soldering" procedure. It contains two non-intersecting subalgebras: $N=2$ superconformal…
To construct ternary "quaternions" following Hamilton we must introduce two "imaginary "units, $q_1$ and $q_2$ with propeties $q_1^n=1$ and $q_2^m=1$. The general is enough difficult, and we consider the $m=n=3$. This case gives us the…
Supersymmetric gauge theories are an important building block for extensions of the standard model. As a first step towards Super-QCD we investigate the pure gauge sector with gluons and gluinos on the lattice, in particular the low energy…
Motivated by the recent high-precision lattice data on Yang-Mills equations of state, we propose an effective theory of SU(3) gluonic matter. The theory is constructed based on the center and scale symmetries and their dynamical breaking,…
We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associative algebra with unity. We find the algebraic relations that…
The purpose of this note is to show that W3 algebras originate from an unusual interplay between the breakings of the reparametrization invariance under the diffemorphism action on the cotangent bundle of a Riemann surface. It is recalled…
Motivated by D-brane scenarios, we consider a non-supersymmetric model based on the gauge symmetry U(3)_CxU(3)_LxU(3)_R$ which is equivalent to the SU(3)^3 ``trinification'' model supplemented by three U(1)s. Two U(1) combinations are…
We construct a canonical basis of two-cycles, on a $K3$ surface, in which the intersection form takes the canonical form $2E_8(-1) \oplus 3H$. The basic elements are realized by formal sums of smooth submanifolds.
A dynamical investigation of the nucleon-nucleon (NN) interaction by using the resonating group method (RGM) in a chiral SU(3) quark model has been revisited. The considered quark-quark interaction includes, besides the one-gluon exchange…