The geometrical basis of PT symmetry
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2018
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MDPI
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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.
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© 2018 by the authors. Licensee MDPI, Basel, Switzerland
Author Contributions: Both authors contributed equally to all aspects of preparing this manuscript.
Funding: Financial support from the Spanish MINECO (Grant No. FIS2015-67963-P) is gratefully acknowledged.
Acknowledgments: We acknowledge illuminating discussions with José María Montesinos.
Conflicts of Interest: The authors declare no conflicts of interest.