391 research outputs found
Heisenberg XXZ Model and Quantum Galilei Group
The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed in
terms of the symmetry given by the quantum Galilei group Gamma_q(1). We show
that the magnon excitations and the s=1/2, n-magnon bound states are determined
by the algebra. Thus the Gamma_q(1) symmetry provides a description that
naturally induces the Bethe Ansatz. The recurrence relations determined by
Gamma_q(1) permit to express the energy of the n-magnon bound states in a
closed form in terms of Tchebischeff polynomials.Comment: (pag. 10
The coisotropic subgroup structure of SL_q(2,R)
We study the coisotropic subgroup structure of standard SL_q(2,R) and the
corresponding embeddable quantum homogeneous spaces. While the subgroups S^1
and R_+ survive undeformed in the quantization as coalgebras, we show that R is
deformed to a family of quantum coisotropic subgroups whose coalgebra can not
be extended to an Hopf algebra. We explicitly describe the quantum homogeneous
spaces and their double cosets.Comment: LaTex2e, 10pg, no figure
Lie Bialgebra Structures for Centrally Extended Two- Dimensional Galilei Algebra and their Lie-Poisson Counterparts
All bialgebra structures for centrally extended Galilei algebra are
classified. The corresponding Lie-Poisson structures on centrally extended
Galilei group are found.Comment: Eq. (11) changed, 15 pages, LaTeX fil
Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group
After a preliminary review of the definition and the general properties of
the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the
quantum plane qP are determined as homogeneous spaces of Fq(E(2)). The
canonical action of Eq(2) is used to define a natural q-analog of the free
Schro"dinger equation, that is studied in the momentum and angular momentum
bases. In the first case the eigenfunctions are factorized in terms of products
of two q-exponentials. In the second case we determine the eigenstates of the
unitary representation, which, in the qP case, are given in terms of Hahn-Exton
functions. Introducing the universal T-matrix for Eq(2) we prove that the
Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix
elements of T, thus giving the correct extension to quantum groups of well
known methods in harmonic analysis.Comment: 19 pages, plain tex, revised version with added materia
Exponential mapping for non semisimple quantum groups
The concept of universal T matrix, recently introduced by Fronsdal and
Galindo in the framework of quantum groups, is here discussed as a
generalization of the exponential mapping. New examples related to
inhomogeneous quantum groups of physical interest are developed, the duality
calculations are explicitly presented and it is found that in some cases the
universal T matrix, like for Lie groups, is expressed in terms of usual
exponential series.Comment: 12 page
On the AKSZ formulation of the Rozansky-Witten theory and beyond
Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action
for the Rozansky-Witten model, which can be defined for any complex manifold
with a closed (2,0)-form. We also construct the holomorphic version of
Rozansky-Witten theory defined over Calabi-Yau 3-fold.Comment: 12 page
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