Induced representations of quantum kinematical algebras

We construct the induced representations of the null-plane quantum Poincar\'e and quantum kappa Galilei algebras in (1+1) dimensions. The induction procedure makes use of the concept of module and is based on the existence of a pair of Hopf algebras with a nondegenerate pairing and dual bases.Comment: 8 pages,LaTeX2e, to be published in the Proceedings of XXIII International Colloquium on Group-Theoretical Methods in Physics, Dubna (Russia), 31.07--05.08, 200

Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics

Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (olmo01), to induce representations of quantum bicrossproduct algebras we construct the representations of the family of standard quantum inhomogeneous algebras $U_\lambda(iso_{\omega}(2))$. This family contains the quantum Euclidean, Galilei and Poincar\'e algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on regular co-spaces that are an algebraic generalization of the homogeneous spaces and $q$--Casimir equations which play the role of $q$--Schr\"odinger equations.Comment: LaTeX 2e, 20 page

RELATIVISTIC-DFT STUDY OF THE ELECTRONIC STRUCTURE, BONDING AND ENERGETIC OF THE [ReF8]־ AND [UF8]2- IONS

Indexación: Web of Science; Scielo.In this study we evaluated the importance of the relativistic effects (scalar and spin-orbit) on the description of the electronic structure, bonding and the energetic of the [ReF8]- and [UF8]2- ions. We described the bonding interaction between ligands and metal center using the energy decomposition analysis (EDA) proposed by Morokuma and Ziegler, in which it can be appreciated a strong ionic behavior for both ions since the electrostatic interaction energy (∆Ezlestat) is greater than the orbitalic interaction energy (∆EOrb). Furthermore, a qualitative analysis using the mapping of the electrostatic potential over the total electronic density evidence an increase of the ionic character, as well as, the polarization of the electronic density as U > Re. The electron localization function (ELF) corroborates the bonding analysis because of the lack of di-synaptic basins on the metal-ligand bonding region.http://ref.scielo.org/jcbd4