Publication: Invisibility and PT Symmetry: A Simple Geometrical Viewpoint
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2014
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MDPI
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Abstract
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via Möbius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.
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Received: 24 February 2014 / Revised: 12 May 2014 / Accepted: 14 May 2014 / Published: 22 May 2014
This article belongs to the Special Issue Physics based on Two-by-two Matrices.