Clifford algebra from quantum automata and unitary Wilson fermions

TL;DR

This paper presents a novel spacetime discretization of the Dirac equation using quantum automata that maintains Clifford algebra invariance and naturally produces unitary Wilson fermions, offering a new approach to lattice gauge theory.

Contribution

It introduces a quantum automaton-based discretization of the Dirac equation that is invariant under Clifford algebra representations and inherently unitary for Wilson fermions.

Findings

Provides a Clifford algebra invariant discretization of the Dirac equation.

Demonstrates natural unitarity of Wilson fermions in the automaton framework.

Offers an alternative to standard lattice gauge theory with improved properties.

Abstract

We introduce a spacetime discretization of the Dirac equation that has the form of a quantum automaton and that is invariant upon changing the representation of the Clifford algebra, as the Dirac equation itself. Our derivation follows Dirac's original one: We required that the square of the discrete Dirac scheme be what we define as an acceptable discretization of the Klein-Gordon equation. Contrary to standard lattice gauge theory in discrete time, in which unitarity needs to be proven, we show that the quantum automaton delivers naturally unitary Wilson fermions for any choice of Wilson's parameter.