  We give a simplified account of the properties of the transfer matrix for a
complex one-dimensional potential, paying special attention to the particular
instance of unidirectional invisibility. In appropriate variables, invisible
potentials appear as performing null rotations, which lead to the
helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can
be interpreted, via M\"{o}bius transformations, as parallel displacements, a
geometric action that has no Euclidean analogy.
