Vectorlike representation of one-dimensional scattering
  We present a self-contained discussion of the use of the transfer-matrix formalism to study one-dimensional scattering. We elaborate on the geometrical interpretation of this transfer matrix as a conformal mapping on the unit disk. By generalizing to the unit disk the idea of turns, introduced by Hamilton to represent rotations on the sphere, we develop a method to represent transfer matrices by hyperbolic turns, which can be composed by a simple parallelogramlike rule. 
L. L. Sanchez-Soto, J. F. Carinena, A. G. Barriuso and J. J. Monzon