Study of information entropy for involved quantum models in complex Cayley-Klein space

Abstract

In the language of the complex formalism, we study the information entropy of a particle on the motion groups from a family of the unitary Cayley-Klein space with constant curvature κ. Hence, in making use of the constant curvature, all the results here presented will be simultaneously valid for the 2D coset space SUκ(2)/U(1) in forms of 2D sphere , hyperbolic plane and Euclidean plane . In addition to physical complex coordinates , their corresponding components are expressed in a 2D complex formalism in terms of the constant curvature in Cayley-Klein space. This process enables us to derive information entropies located in the circular well on two spaces, which are the basis for achieving the relationship between Shannon entropy and Fisher information and the inequalities among them. In particular, we notice that the particle has freely behavior in a spherical state , while it behaves as a constraint particle in the situation of the hyperbolic plane .