TRANSLATIONS AND INVERSIONS IN FINITE PHASE PLANE

The inversion operators on a lattice in finite phase plane are used for building a complete set of mutually orthogonal Hermitian operators. The lattice is given by tc in the x direction and by in the p-direction; c is an arbitrary length constant and M is the dimension of the space; s and t assume the values from 0 to M – 1. For M odd the M² inversion operators on the lattice form a complete set of mutually orthogonal operators. For M even we assign a sum of 4 inversion operators (a quartet) to each site of the lattice (t, s). We prove that these quartets for t, s = 0, 1, … ,M – 1 form a mutually orthogonal set of M² Hermitian operators.