Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

Luis L. Sanchez-Soto, Juan J. Monzon

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 Mobius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.

Quantum Physics (quant-ph)

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