Quantum walks, deformed relativity, and Hopf algebra symmetries

TL;DR

This paper explores how Weyl quantum walks with nonlinear Lorentz symmetry can be described using Hopf algebra structures, specifically Poincaré and k-Poincaré algebras, to understand particle dynamics.

Contribution

It introduces a framework linking quantum walks with Hopf algebra symmetries, extending the understanding of deformed relativity models.

Findings

Hopf algebra structures can describe quantum walk symmetries

Two models of Hopf algebras are analyzed: Poincaré and k-Poincaré

The approach connects quantum walks with deformed relativistic 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 Poincar\'e and the k-Poincar\'e algebras.