We show that h-deformation can be obtained, by a singular limit of a similarity transformation, from q-deformation; to be specefic, we obtain GL h (2), its differential structure, its inhomogenous extension, and U h (sl(2)) from their q-deformed counterparts.The idea of using singular limits of transformations is not new. Contraction of Lie groups, as first introduced by Inonu and Wigner [1] is such a process. This contraction procedure has been successfully applied to quantum groups to obtain deformations of inhomogeneous groups like E q (2) and the Poincaré group [2][3][4].In this letter, we will show that h-deformation [5-13] can be obtained from q-deformation by a singular limit of a similarity transformation. Not only the Hopf algebras but also the whole differential structure is obtained in this way. Besides, this is also true for the inhomogeneous quantum group IGL h (2) which can be obtained from IGL q (2).Before describing the contraction procedure, it is worth mentioning why GL q (2) and GL h (2) and their two-parametric generalizations are imortant. First, the only quantum groups which preserve nondegenerate bilinear forms are GL q p (2) and GL h h ′ (2), [5,13]. These 1
Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been obtained.
Using the Einstein-Cartan-Dirac theory, we study the effect of torsion on neutrino oscillation. We see that torsion cannot induce neutrino oscillation, but affects it whenever oscillation exists for other reasons. We show that the torsion effect on neutrino oscillation is as important as the neutrino mass effect, whenever the ratio of neutrino number density to neutrino energy is ∼ 10 69 cm −3 /eV, or the number density of the matter is ∼ 10 69 cm −3 .
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