Invisibility and Symmetry: A Simple Geometrical Viewpoint

Symmetry

Luis L. Sánchez-Soto¹ 

关键词: PT symmetry;    SL(2;    ℂ);    Lorentz group;    Hyperbolic geometry;   

DOI  :  10.3390/sym6020396

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.