Mathematics – Quantum Algebra
Scientific paper
2002-02-12
J.Phys.A35:8449-8466,2002
Mathematics
Quantum Algebra
LaTeX 2e, 20 pages
Scientific paper
10.1088/0305-4470/35/40/306
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.
Arratia Oscar
del Olmo Mariano A.
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