Invisibility and PT Symmetry: A Simple Geometrical Viewpoint
  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. 
Luis L. Sanchez-Soto and Juan J. Monzon
quant-ph