# Position and momentum bases for the monochromatic Maxwell fish-eye and the sphere

@article{SaltoAlegre2015PositionAM, title={Position and momentum bases for the monochromatic Maxwell fish-eye and the sphere}, author={Cristina Salto-Alegre and Kurt Bernardo Wolf}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2015}, volume={48} }

In geometric optics the Maxwell fish-eye is a medium where light rays follow circles, while in scalar wave optics this medium can only ‘trap’ fields of certain discrete frequencies. In the monochromatic case characterized by a positive integer ℓ, there are 2 ℓ + 1 ?> independent fields. We identify two bases of functions: one, known as the Sherman–Volobuyev functions, is characterized as of ‘most definite’ momenta; the other is new and composed of ‘most definite’ positions and normal…

## One Citation

SU(2)-particle sigma model: momentum-space quantization of a particle on the sphere S3

- Physics, MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

We perform the momentum-space quantization of a spin-less particle moving on the group manifold, that is, the three-dimensional sphere S3, by using a non-canonical method entirely based on symmetry…

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