Klein-Gordon equation in $q$-deformed Euclidean space

Abstract

We introduce q-versions of the Klein-Gordon equation in the threedimensional q-deformed Euclidean space. We determine plane wave solutions to our q-deformed Klein-Gordon equations. We show that these plane wave solutions form a complete orthogonal system. We discuss the propagators of our q-deformed Klein-Gordon equations. We derive continuity equations for the charge density, the energy density, and the momentum density of a q-deformed spin-zero particle.