Quantum walks, deformed relativity, and Hopf algebra symmetries

Abstract

We show how the Weyl quantum walk derived from principles in Ref. [1], enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras--the usual Poincaré and the k-Poincaré algebras.

11 pages. Published version. The present article supersedes arXiv:1503.01017