ARTICLE | doi:10.20944/preprints201810.0270.v1
Subject: Physical Sciences, Optics And Photonics Keywords: PPT symmetry; SL(2, C); hyperbolic geometry
Online: 12 October 2018 (12:42:28 CEST)
We reelaborate on the basic properties of PT symmetry from a geometrical Perspective. The transfer matrix associated with these systems induces a Möbius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.