  Gauge invariance is one of the more important concepts in physics. We discuss
this concept in connection with the unitary evolution of discrete-time quantum
walks in one and two spatial dimensions, when they include the interaction with
synthetic, external electromagnetic fields. One introduces this interaction as
additional phases that play the role of gauge fields. Here, we present a way to
incorporate those phases, which differs from previous works. Our proposal
allows the discrete derivatives, that appear under a gauge transformation, to
treat time and space on the same footing, in a way which is similar to standard
lattice gauge theories. By considering two steps of the evolution, we define a
density current which is gauge invariant and conserved. In the continuum limit,
the dynamics of the particle, under a suitable choice of the parameters,
becomes the Dirac equation, and the conserved current satisfies the
corresponding conservation equation.
