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

Understand

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.