Sánchez-Soto, L.L.; Monzón, J.J. The Geometrical Basis of PT Symmetry. Symmetry2018, 10, 494.
Sánchez-Soto, L.L.; Monzón, J.J. The Geometrical Basis of PT Symmetry. Symmetry 2018, 10, 494.
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.
PPT symmetry; SL(2, C); hyperbolic geometry
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