Symplectic Covariance of Phase Point Operator on Discrete Space

Abstract

The phase point operator 0(q, p) is a quantum counterpart of classical phase point (q, p) . Its discrete version was formulated for an odd number of lattice points by Cohendet et al. and even case by Leonhardt. They both have symplectic covariance which is of fundamental importance in quantum mechanics. But its explicit form of the projective representation of the symplectic group which appears in the covariance relation is not yet known. We show in this paper the existence and uniqueness of the representation and a method to construct it using the Euclidean algorithm