Quantum walks, deformed relativity and Hopf algebra symmetries
Alessandro Bisio, Giacomo Mauro D'Ariano, Paolo Perinotti · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 2016
We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), 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 theκ-Poincaré algebras.