Related papers: A Little Large N Group Theory
We discuss properties of QCD with variable and large $N_c$, taking into account electroweak interactions; i.e., we analyze the generalization of the standard model based on the gauge group $G={\rm SU}(N_c) \times {\rm SU(2)}_L \times {\rm…
We formulate Poisson Chern-Simons gauge theories on compact group manifolds. These describe a sector of the large representation limit of noncommutative Chern-Simons in the same way as the light-cone formulation of the membrane action…
We present a non-relativistic fermionic field theory in 2-dimensions coupled to external gauge fields. The singlet sector of the $c=1$ matrix model corresponds to a specific external gauge field. The gauge theory is one-dimensional (time)…
We study the properties and couplings of hybrid baryons in the large-$N_c$ expansion. These are color-neutral baryon states which contain in addition to $N_c$ quarks also one constituent gluon. Hybrid baryons with both symmetric and mixed…
We show that with respect to the Haar state, the joint distributions of the generators of Van Daele and Wang's free orthogonal quantum groups are modeled by free families of generalized circular elements and semicircular elements in the…
We discuss the common features between the Standard Model taxonomy of particles, based on electric charge, strangeness and isospin, and the taxonomy emerging from the key structural elements of the rotating neutrino model, which describes…
We give a uniform construction of irreducible polynomial representations of all classical groups, including spin groups, using semistandard domino tableaux. We also give an explicit decomposition of the homogeneous coordinate ring of the…
We describe a new exact relation for large $N_c$ QCD for the long-distance behavior of baryon form factors in the chiral limit, satisfied by all 4D semi-classical chiral soliton models. We use this relation to test the consistency of the…
In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups…
Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…
We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…
We introduce the notion of Glanon groupoids, which are Lie groupoids equipped with multiplicative generalized complex structures. It combines symplectic groupoids, holomorphic Lie groupoids and holomorphic Poisson groupoids into a unified…
It is common practice to describe elementary particles by irreducible unitary representations of the Poincar\'e group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincar\'e group.…
In QCD one can change the representation of the gauge group for quarks and/or the gauge group itself. Examples of such generalizations are: (a) supersymmetric Yang-Mills theory with gauge group SU(2) or SU(3); (b) QCD with SU(2) colour and…
Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…
A systematic study of large N expansion in supersymmetric theories are given. Supersymmetric O(N) non-linear sigma model in two and three dimensions, massless and massive supersymmetric QCD with $N_{f}<N_{c}-1$ and supergravity models are…
Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields…
Quantum fields are considered as generators of infinite-dimensional Clifford algebra $Cl(\infty)$, which can be either orthogonal (in case of fermions) or symplectic (in case of bosons). A generic quantum state can be expressed as a…
We consider 1+1-dimensional QCD coupled to Majorana fermions in the adjoint representation of the gauge group $SU(N)$. Pair creation of partons (fermion quanta) is not suppressed in the large-$N$ limit, where the glueball-like bound states…
A new set of polynomial states (to be called character states) are derived for $Sp(4)$ reduced to its $SU(2) \times U(1)$ subgroup, and the relevant generator matrix elements are evaluated for generic representations $(a,b)$ of $Sp(4)$.…