Details

Autor(en) / Beteiligte

• Frank, Alejandro
• Leyvraz, François
• Wolf, Kurt Bernardo

Titel

Hidden symmetry and potential group of the Maxwell fish‐eye

Ist Teil von

• Journal of mathematical physics, 1990-12, Vol.31 (12), p.2757-2768

Erscheinungsjahr

1990

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The Maxwell fish‐eye is an exceptional optical system that shares with the Kepler problem and the point rotor (mass point on a sphere) a hidden, higher rotation symmetry. The Hamiltonian is proportional to the Casimir invariant. The well‐known stereographic map is extended to c a n o n i c a l transformations between of the phase spaces of the constrained rotor and the fish‐eye. Their d y n a m i c a l group is a pseudoorthogonal one that permits a succint ‘‘4π’’ wavization of the constrained system. The fish‐eye exhibits, unavoidably, chromatic dispersion. Further, a larger conformal dynamical group contains the p o t e n t i a l group, that relates the closed, inhomogeneous fish‐eye system to similar, scaled ones. Asymptotically, it is related to free propagation in homogenous media.