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Free keywords:
PT symmetry; SL(2, C); hyperbolic geometry
Abstract:
We reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Mobius 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.
