N ov 1 99 9 LYCEN 9121 June 1991 ON QUANTUM GROUPS AND THEIR POTENTIAL USE IN MATHEMATICAL CHEMISTRY ∗
نویسندگان
چکیده
The quantum algebra su q (2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of q-bosons. In connection with the quantum algebra su q (2), we discuss the q-analogues of the harmonic oscillator and the angular momentum. We also introduce q-analogues of the hydrogen atom by means of a q-deformation of the Pauli equations and of the so-called Kustaanheimo-Stiefel transformation.
منابع مشابه
ar X iv : q - a lg / 9 71 10 27 v 1 2 8 N ov 1 99 7 Yang – Baxter systems , solutions and applications
Two types of Yang–Baxter systems play roles in the theoretical physics – constant and colour dependent. The constant systems are used mainly for construction of special Hopf algebra while the colour or spectral dependent for construction of quantum integrable models. Examples of both types together with their particular solutions are presented. The complete solution is known only for the consta...
متن کامل06 7 v 1 1 9 D ec 1 99 1 ON THE SYMMETRIES OF INTEGRABILITY
We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group A (1) 2. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of sym...
متن کامل6 v 1 1 N ov 1 99 4 Many q - Particles from One : a New Approach to ∗ - Hopf Algebras ?
We propose a nonstandard approach to solving the apparent incompatibility between the coalgebra structure of some inhomogeneous quantum groups and their natural complex conjugation. In this work we sketch the general idea and develop the method in detail on a toy-model; the latter is a q-deformation of the Hopf algebra of 1-dim translations + dilatations. We show how to get all Hilbert space re...
متن کامل2 v 3 2 4 N ov 1 99 5 The Real Symplectic Groups in
1 Abstract We present a utilitarian review of the family of matrix groups Sp(2n, ℜ), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Eu-clidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-calle...
متن کاملv 1 5 N ov 1 99 7 TWO - STRUCTURE FRAMEWORK FOR HAMILTONIAN DYNAMICAL SYSTEMS ∗
The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group of the order automorphisms (Lie algebras with invariant cones). Taking advantage of the reciprocal independence of the relevant structures, the inclusion rela...
متن کامل