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

@article{Wolf2011TheFU, title={The Fourier U(2) Group and Separation of Discrete Variables}, author={Kurt Bernardo Wolf and Luis Edgar Vicent}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2011}, volume={7}, pages={053} }

The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4;<), whose maximal compact subgroup is the Fourier group U(2) F ; this includes isotropic and anisotropic Fourier transforms, screen rotations and gy- rations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the…

## 4 Citations

### Finite optical Hamiltonian systems

- PhysicsInternational Commission for Optics
- 2011

In this essay we finitely quantize the Hamiltonian system of geometric optics to a finite system that is also Hamiltonian, but where signals are described by complex N-vectors, which are subject to…

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The Fourier group U(2)F is the maximal compact group of the group of linear canonical transformations on configuration space. When we finitely quantize the two-dimensional harmonic oscillator we turn…

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- Environmental ScienceJournal of the Optical Society of America A
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Unitary rotations of polychromatic images on finite two-dimensional pixellated screens provide invertibility, group composition, and thus conservation of information. Rotations have been applied on…

### Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors

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Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdicka-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher…

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