Lorentz covariance of lattice field equations in four-dimensional space-time

Abstract

It is noted that lattice field equations in discrete four-dimensional space-time admit $k$-space covariance under appropriate nonlinear representations of the Lorentz group. By explicit use of a vierbein field, it is made evident that the Lorentz covariance in $k$ space is exclusively "passive" and cannot be implemented with an "active" Lorentz transformation from one inertial frame to another, like that associated with the usual (linear) $x$-space Lorentz transformation.