A New Algebraic Structure of Finite Quantum Systems and the Modified Bessel Functions

Details A New Algebraic Structure of Finite Quantum Systems and the Modified Bessel Functions A New Algebraic Structure of Finite Quantum Systems and the Modified Bessel Functions

2007-04-14

arxiv.org/abs/0704.1844v2

Int.G.Geom.Meth.Mod.Phys. 4(2007) 1205-1215

Physics

Quantum Physics

Latex ; 14 pages ; no figure ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics, (Vo.4

Scientific paper

In this paper we present a new algebraic structure (a super hyperbolic system in our terminology) for finite quantum systems, which is a generalization of the usual one in the two-level system. It fits into the so-called generalized Pauli matrices, so they play an important role in the theory. Some deep relation to the modified Bessel functions of integer order is pointed out. By taking a skillful limit finite quantum systems become quantum mechanics on the circle developed by Ohnuki and Kitakado.

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