A discrete relativistic spacetime formalism for 1+1-QED with continuum limits

TL;DR

This paper introduces a quantum cellular automaton model that accurately reproduces 1+1 QED and the Dirac equation in the continuum limits, providing a discrete spacetime framework for relativistic quantum field theories.

Contribution

A novel quantum cellular automaton model for 1+1 QED that converges to known continuum theories in the appropriate limits.

Findings

QCA reproduces 1+1 QED in continuum limit

Model converges to Dirac equation in free particle sector

Maintains U(1) gauge invariance

Abstract

We build a quantum cellular automaton (QCA) which coincides with 1+1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut-Susskind staggered version of 1+1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation, a strong indication that the model remains accurate in the relativistic regime.