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

Abstract

We introduce $q$-versions of the Klein-Gordon equation in the three-dimensional $q$-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.

44 pages, 4 figures, the appendix contains material from previous articles. arXiv admin note: text overlap with arXiv:2010.08826, arXiv:2103.03356