Title: Galois fields in quantum mechanics
Abstract: A quantum system where the position and momentum take values in the Galois field GF(p^n), is considered. The Heisenberg-Weyl group of displacements and the symplectic group Sp(2,GF(p^n)) of symplectic transformations, are studied. Frobenius symmetries is a unique feature of these systems, which has no analogue in the harmonic oscillator formalism. Quantum engineering of these systems from a chain of j=(p-1)/2 spins which are coupled in a special way, is discussed.