Article
Version 1
Preserved in Portico This version is not peer-reviewed
The Geometrical Basis of PT Symmetry
Version 1
: Received: 24 September 2018 / Approved: 12 October 2018 / Online: 12 October 2018 (12:42:28 CEST)
A peer-reviewed article of this Preprint also exists.
Sánchez-Soto, L.L.; Monzón, J.J. The Geometrical Basis of PT Symmetry. Symmetry 2018, 10, 494. Sánchez-Soto, L.L.; Monzón, J.J. The Geometrical Basis of PT Symmetry. Symmetry 2018, 10, 494.
Abstract
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.
Keywords
PPT symmetry; SL(2, C); hyperbolic geometry
Subject
Physical Sciences, Optics and Photonics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
