1,195 research outputs found
The exponential map for representations of
For the quantum group and the corresponding quantum algebra
Fronsdal and Galindo explicitly constructed the so-called
universal -matrix. In a previous paper we showed how this universal
-matrix can be used to exponentiate representations from the quantum algebra
to get representations (left comodules) for the quantum group. Here, further
properties of the universal -matrix are illustrated. In particular, it is
shown how to obtain comodules of the quantum algebra by exponentiating modules
of the quantum group. Also the relation with the universal -matrix is
discussed.Comment: LaTeX-file, 7 pages. Submitted for the Proceedings of the 4th
International Colloquium ``Quantum Groups and Integrable Systems,'' Prague,
22-24 June 199
The quantum superalgebra : deformed para-Bose operators and root of unity representations
We recall the relation between the Lie superalgebra and para-Bose
operators. The quantum superalgebra , defined as usual in terms
of its Chevalley generators, is shown to be isomorphic to an associative
algebra generated by so-called pre-oscillator operators satisfying a number of
relations. From these relations, and the analogue with the non-deformed case,
one can interpret these pre-oscillator operators as deformed para-Bose
operators. Some consequences for (Cartan-Weyl basis,
Poincar\'e-Birkhoff-Witt basis) and its Hopf subalgebra are
pointed out. Finally, using a realization in terms of ``-commuting''
-bosons, we construct an irreducible finite-dimensional unitary Fock
representation of and its decomposition in terms of
representations when is a root of unity.Comment: 15 pages, LaTeX (latex twice), no figure
Unitarizable Representations of the Deformed Para-Bose Superalgebra Uq[osp(1/2)] at Roots of 1
The unitarizable irreps of the deformed para-Bose superalgebra , which
is isomorphic to , are classified at being root of 1. New
finite-dimensional irreps of are found. Explicit expressions
for the matrix elements are written down.Comment: 19 pages, PlainTe
Dynamics in a noncommutative phase space
Dynamics has been generalized to a noncommutative phase space. The
noncommuting phase space is taken to be invariant under the quantum group
. The -deformed differential calculus on the phase space is
formulated and using this, both the Hamiltonian and Lagrangian forms of
dynamics have been constructed. In contrast to earlier forms of -dynamics,
our formalism has the advantage of preserving the conventional symmetries such
as rotational or Lorentz invariance.Comment: LaTeX-twice, 16 page
Real Space Renormalization Group Study of the S=1/2 XXZ Chains with Fibonacci Exchange Modulation
Ground state properties of the S=1/2 antiferromagnetic XXZ chain with
Fibonacci exchange modulation are studied using the real space renormalization
group method for strong modulation. The quantum dynamical critical behavior
with a new universality class is predicted in the isotropic case. Combining our
results with the weak coupling renormalization group results by Vidal et al.,
the ground state phase diagram is obtained.Comment: 9 pages, 9 figure
Quantum critical behavior of disordered itinerant ferromagnets
The quantum ferromagnetic transition at zero temperature in disordered
itinerant electron systems is considered. Nonmagnetic quenched disorder leads
to diffusive electron dynamics that induces an effective long-range interaction
between the spin or order parameter fluctuations of the form r^{2-2d}, with d
the spatial dimension. This leads to unusual scaling behavior at the quantum
critical point, which is determined exactly. In three-dimensional systems the
quantum critical exponents are substantially different from their finite
temperature counterparts, a difference that should be easily observable.
Experiments to check these predictions are proposed.Comment: 14pp., REVTeX, 3 eps figs, final version as publishe
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