Unitary Operator Bases and Q-deformed Algebras

Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commutation relation is shown to emerge in a natural way, when the deformation parameter is a root of unity.

Irreducibility and compositeness in q-deformed harmonic oscillator algebras

A study of the reducibility of the Fock space representation of the q-deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is carried out by using the properties of the Gauss polynomials. When the deformation parameter is a root of unity, an interesting result comes out in the form of a reducibility scheme for the space representation which is based on the classification of the primitive or nonprimitive character of the deformation parameter. An application is carried out for a q-deformed harmonic oscillator Hamiltonian, to which the reducibility scheme is explicitly applied.

MANY-BODY PROBLEMS WITH COMPOSITE-PARTICLES AND Q-HEISENBERG ALGEBRAS

We propose to employ deformed commutation relations to treat many-body problems of composite particles. The deformation parameter is interpreted as a measure of the effects of the statistics of the internal degrees of freedom of the composite particles. A simple application of the method is made for the case of a gas of composite bosons.

Q-deformed fermionic Lipkin model at finite temperature

The interplay between temperature and q-deformation in the phase transition properties of many-body systems is studied in the particular framework of the collective q-deformed fermionic Lipkin model. It is shown that in phase transitions occuring in many-fermion systems described by su(2)q-like models are strongly influenced by the q-deformation.

A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

PHASE-TRANSITION IN A Q-DEFORMED LIPKIN MODEL

Assuming q-deformed commutation relations for the fermions, an extension of the standard Lipkin Hamiltonian is presented. The usual quasi-spin representation of the standard Lipkin model is also obtained in this q-deformed framework. A variationally obtained energy functional is used to analyse the phase transition associated with the spherical symmetry breaking. The only phase transitions in this q-deformed model are of second order. As an outcome of this analysis a critical parameter is obtained which is dependent on the deformation of the algebra and on the number of particles.

Non-Abelian Sugawara construction and the q-deformed N=2 superconformal algebra

The construction of a q-deformed N = 2 superconformal algebra is proposed in terms of level-1 currents of the U-q(<(su)over cap>(2)) quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed energy-momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to U-q(<(su)over cap>(N + 1)) is also proposed.

An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

q-deformed variational study of the Lipkin-Meshkov-Glick model via coherent states

We show that the ground-state energy of the q-deformed Lipkin-Meshkov-Glick Hamiltonian can be estimated by q-deformed coherent states. We also use these coherent states to analyse qualitatively the suppression of the second order ground-state energy phase transition of this model. © 1993.

Operator formulation of q-deformed dual string model

We present an operator formulation of the q-deformed dual string model amplitude using an infinite set of q-harmonic oscillators. The formalism attains the crossing symmetry and factorization and allows to express the general n-point function as a factorized product of vertices and propagators.

Hamiltonian reduction and the construction of q-deformed extensions of the Virasoro algebra

In this paper we employ the construction of the Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-Wess-Zumino-Witten model and the Liouville theory are imposed to show that it satisfies the q-Virasoro algebra proposed by Frenkel and Reshetikhin The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.

q-Leibniz Algebras

2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25.

Localization of quantum biequivariant D-modules and q-W algebras

Peer reviewed