Quantum walks, deformed relativity and Hopf algebra symmetries

Alessandro Bisio; Giacomo Mauro D'Ariano; Paolo Perinotti

doi:10.1098/rsta.2015.0232

Quantum walks, deformed relativity and Hopf algebra symmetries

Philos Trans A Math Phys Eng Sci. 2016 May 28;374(2068):20150232. doi: 10.1098/rsta.2015.0232.

Authors

Alessandro Bisio¹, Giacomo Mauro D'Ariano², Paolo Perinotti²

Affiliations

¹ QUIT group, Dipartimento di Fisica, Università degli Studi di Pavia, and INFN, Gruppo IV, via Bassi 6, 27100 Pavia, Italy dariano@unipv.it.
² QUIT group, Dipartimento di Fisica, Università degli Studi di Pavia, and INFN, Gruppo IV, via Bassi 6, 27100 Pavia, Italy.

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.

Keywords: Hopf algebras; doubly special relativity; quantum walks.

Publication types

Research Support, Non-U.S. Gov't