The Fourier U(2) Group and Separation of Discrete Variables

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• Main Author: Wolf, K.B.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147171
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Fourier U(2) Group and Separation of Discrete Variables / K.B. Wolf, L.E. Vicent // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ.

The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R), whose maximal compact subgroup is the Fourier group U(2)F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and op...