68 research outputs found
Reflection equations and q-Minkowski space algebras
We express the defining relations of the -deformed Minkowski space algebra
as well as that of the corresponding derivatives and differentials in the form
of reflection equations. This formulation encompasses the covariance properties
with respect the quantum Lorentz group action in a straightforward way.Comment: 10 page
A note on graded Yang-Baxter solutions as braid-monoid invariants
We construct two solutions of the graded Yang-Baxter equation by
using the algebraic braid-monoid approach. The factorizable S-matrix
interpretation of these solutions is also discussed.Comment: 7 pages, UFSCARF-TH-94-1
PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields
The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to
be quasi-Hermitian for special values of the boundary parameters. This is
proved by explicit construction of a new inner product employing a
"quasi-fermion" algebra in momentum space where creation and annihilation
operators are not related via Hermitian conjugation. For a special example,
when the boundary fields lie on the imaginary axis, we show the spectral
equivalence of the quasi-Hermitian XX spin-chain with a non-local fermion
model, where long range hopping of the particles occurs as the non-Hermitian
boundary fields increase in strength. The corresponding Hamiltonian
interpolates between the open XX and the quantum group invariant XXZ model at
the free fermion point. For an even number of sites the former is known to be
related to a CFT with central charge c=1, while the latter has been connected
to a logarithmic CFT with central charge c=-2. We discuss the underlying
algebraic structures and show that for an odd number of sites the superalgebra
symmetry U(gl(1|1)) can be extended from the unit circle along the imaginary
axis. We relate the vanishing of one of its central elements to the appearance
of Jordan blocks in the Hamiltonian.Comment: 37 pages, 5 figure
Deformed Minkowski spaces: clasification and properties
Using general but simple covariance arguments, we classify the `quantum'
Minkowski spaces for dimensionless deformation parameters. This requires a
previous analysis of the associated Lorentz groups, which reproduces a previous
classification by Woronowicz and Zakrzewski. As a consequence of the unified
analysis presented, we give the commutation properties, the deformed (and
central) length element and the metric tensor for the different spacetime
algebras.Comment: Some comments/misprints have been added/corrected, to appear in
Journal of Physics A (1996
Fermion-Boson Interactions and Quantum Algebras
Quantum Algebras (q-algebras) are used to describe interactions between
fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry
is invoked in order to reproduce the ground state properties of systems of
fermions and bosons interacting via schematic forces. The structure of the
proposed su_q(2) Hamiltonians, and the meaning of the corresponding deformation
parameters, are discussed.Comment: 20 pages, 10 figures. Physical Review C (in press
Quantum Deformed Algebra and Superconformal Algebra on Quantum Superspace
We study a deformed algebra on a quantum superspace. Some
interesting aspects of the deformed algebra are shown. As an application of the
deformed algebra we construct a deformed superconformal algebra. {}From the
deformed algebra, we derive deformed Lorentz, translation of
Minkowski space, and its supersymmetric algebras as closed
subalgebras with consistent automorphisms.Comment: 27 pages, KUCP-59, LaTeX fil
On factorization of q-difference equation for continuous q-Hermite polynomials
We argue that a customary q-difference equation for the continuous q-Hermite
polynomials H_n(x|q) can be written in the factorized form as (D_q^2 -
1)H_n(x|q)=(q^{-n}-1)H_n(x|q), where D_q is some explicitly known q-difference
operator. This means that the polynomials H_n(x|q) are in fact governed by the
q-difference equation D_qH_n(x|q)=q^{-n/2}H_n(x|q), which is simpler than the
conventional one.Comment: 7 page
Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs
We present formulas for the Clebsch-Gordan coefficients and the Racah
coefficients for the root of unity representations (-dimensional
representations with ) of . We discuss colored vertex
models and colored IRF (Interaction Round a Face) models from the color
representations of . We construct invariants of trivalent colored
oriented framed graphs from color representations of .Comment: 39 pages, January 199
Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
The minimal twist map introduced by B. Abdesselam, A. Chakrabarti, R.
Chakrabarti and J. Segar (Mod. Phys. Lett. A 14 (1999) 765) for the
non-standard (Jordanian) quantum sl(2,R) algebra is used to construct the twist
maps for two different non-standard quantum deformations of the (1+1)
Schrodinger algebra. Such deformations are, respectively, the symmetry algebras
of a space and a time uniform lattice discretization of the (1+1) free
Schrodinger equation. It is shown that the corresponding twist maps connect the
usual Lie symmetry approach to these discrete equations with non-standard
quantum deformations. This relationship leads to a clear interpretation of the
deformation parameter as the step of the uniform (space or time) lattice.Comment: 16 pages, LaTe
Discrete quantum model of the harmonic oscillator
We construct a new model of the quantum oscillator, whose energy spectrum is
equally-spaced and lower-bounded, whereas the spectra of position and momentum
are a denumerable non-degenerate set of points in [-1,1] that depends on the
deformation parameter q from (0,1). We provide its explicit wavefunctions, both
in position and momentum representations, in terms of the discrete q-Hermite
polynomials. We build a Hilbert space with a unique measure, where an analogue
of the fractional Fourier transform is defined in order to govern the time
evolution of this discrete oscillator. In the limit q to 1, one recovers the
ordinary quantum harmonic oscillator.Comment: 21 page
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