2022/08/31 by Arnault, Pablo, Cedzich, Christopher
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2208.14997
We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is hence inherently unitary and strictly local, i.e., transition amplitudes exactly vanish outside of a lightcone on the lattice. We then provide a lattice Noether's theorem for internal symmetries of this action. We further couple this action to an electromagnetic field by a minimal substitution on the lattice. Finally, we suggest a real-time lattice-gauge-theory-type action for the electromagnetic field in arbitrary spacetime dimensions, and derive its classical equations of motion, which are lattice versions of Maxwell's equations.