A New Algebraic Structure of Finite Quantum Systems and the Modified Bessel Functions
arXiv:0704.1844 · doi:10.1142/S021988780700251X
Abstract
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.
Latex ; 14 pages ; no figure ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics, (Vo.4, No.7), 2007