Discrete Feynman propagator for the Weyl quantum walk in 2+1 dimensions

TL;DR

This paper derives an analytical discrete Feynman propagator for the Weyl quantum walk in 2+1 dimensions, providing a path-integral formulation that could extend to higher dimensions, advancing the understanding of relativistic quantum dynamics.

Contribution

It presents the first analytical solution of the Weyl quantum walk in 2+1 dimensions using a discrete path-integral approach based on binary path encoding.

Findings

Derived the discrete Feynman propagator for 2+1D Weyl walk

Introduced a binary encoding of paths on the lattice

Opened prospects for solutions in 3+1 dimensions

Abstract

Recently quantum walks have been considered as a possible fundamental description of the dynamics of relativistic quantum fields. Within this scenario we derive the analytical solution of the Weyl walk in 2+1 dimensions. We present a discrete path-integral formulation of the Feynman propagator based on the binary encoding of paths on the lattice. The derivation exploits a special feature of the Weyl walk, that occurs also in other dimensions, that is closure under multiplication of the set of the walk transition matrices. This result opens the perspective of a similar solution in the 3+1 case.