Related papers: Birdtracks for SU(N)
For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint…
We classify self-adjoint first-order differential operators on weighted Bergman spaces on the unit disc and answer questions related to uncertainty principles for such operators. Our main tools are the discrete series representations of…
We report on our recent results regarding numerical simulations of the four dimensional, N=1 Supersymmetric Yang-Mills theory with SU(3) gauge symmetry and light dynamical gluinos.
In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of…
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operads obtained from usual monoids such as the additive and multiplicative…
A new approach to massive integrable models is considered. It allows one to find symmetry algebras which define spaces of local operators and to get general integral representations for form-factors in the\ $ SU(2)$\ Thirring and…
This is Part I of a series of papers constructing intertwining operator superalgebras and vertex tensor categories associated to the superconformal minimal models and other related models. In this paper, we construct the intertwining…
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar…
Small momenta limit of the lattice color dielectric model in the SU(3)_c case is considered. We show that in that limit the model involves a coarse-grained gluon field, a color singlet "bleached gluon" field, and both color singlet and…
We illustrate how QCD color structure elegantly can be decomposed into orthogonal multiplet bases corresponding to irreducible representations of SU(Nc) with the aid of Wigner 3j and 6j coefficients. We also show how to calculate the…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
Complete spectra of the staggered Dirac operator $\Dirac$ are determined in four-dimensional $SU(2)$ gauge fields with and without dynamical fermions. An attempt is made to relate the performance of multigrid and conjugate gradient…
The evidence for neutrino masses in atmospheric and solar neutrino experiments provides further support for the embedding of the Standard Model fermions in the chiral 16 SO(10) representation. Such an embedding is afforded by the realistic…
We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which…
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…
The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into…
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
We introduce an effort to catalog the gauge-invariant interactions of Standard Model (SM) particles and new fields in a variety of representations of the SM color gauge group $\text{SU}(3)_{\text{c}}$. In this first installment, we direct…
We investigate the spectral flows of the hermitian Wilson-Dirac operator in the fundamental and adjoint representations on two ensembles of pure SU(2) gauge field configurations at the same physical volume. We find several background gauge…
We linearize nonlinear supersymmetry in the Volkov-Akulov (VA) theory for extended SUSY in two dimensional spacetime ($d = 2$) based on the commutator algebra. Linear SUSY transformations of basic component fields for general vector…