title: Quantum walks, deformed relativity and Hopf algebra symmetries.
abstract: 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.
authors.affiliation: QUIT group, Dipartimento di Fisica, Università degli Studi di Pavia, and INFN, Gruppo IV, via Bassi 6, 27100 Pavia, Italy dariano@unipv.it.
authors.forename: Alessandro
authors.identifier: http://orcid.org/0000-0002-9356-3448
authors.initials: A
authors.lastname: Bisio
authors.affiliation: QUIT group, Dipartimento di Fisica, Università degli Studi di Pavia, and INFN, Gruppo IV, via Bassi 6, 27100 Pavia, Italy.
authors.forename: Giacomo Mauro
authors.identifier: http://orcid.org/0000-0003-0602-5519
authors.initials: GM
authors.lastname: D'Ariano
authors.affiliation: QUIT group, Dipartimento di Fisica, Università degli Studi di Pavia, and INFN, Gruppo IV, via Bassi 6, 27100 Pavia, Italy.
authors.forename: Paolo
authors.identifier: http://orcid.org/0000-0003-4825-4264
authors.initials: P
authors.lastname: Perinotti
keywords: Hopf algebras; doubly special relativity; quantum walks