Preprint Article Version 1 This version is not peer-reviewed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.

Journal reference: Symmetry 2018, 10, 494
DOI: 10.3390/sym10100494

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.

Subject Areas

PPT symmetry; SL(2, C); hyperbolic geometry

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