Scattering of a particle on the -deformed Euclidean space
arXiv:2208.05723
Abstract
We develop a formalism for the scattering of a particle on the -deformed Euclidean space. We write down -versions of the Lippmann-Schwinger equation. Their iterative solutions for a weak scattering potential lead us to -versions of the Born series. With the expressions for the wave functions of the scattered particle, we can write down S-matrix elements. We show that these S-matrix elements satisfy unitarity conditions. Considerations about the interaction picture for a quantum system in the -deformed Euclidean space and a discussion of a -version of time-dependent perturbation theory conclude our studies.
47 pages, 3 figures, the appendix contains material from previous articles. arXiv admin note: text overlap with arXiv:2010.08826, arXiv:2201.01292