Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

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 hel...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry (Basel) 2014-06, Vol.6 (2), p.396-408
Main Authors: Sánchez-Soto, Luis, Monzón, Juan
Format: Article
Language:English
Subjects:
Analogies
Euclidean geometry
Geometric transformation
Hyperbolic geometry
Lorentz group
SL(2, C)
Symmetry
Visibility
ΡT symmetry
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym6020396