From Fermat principle to the Lobačevskii-Fok space in particle physics

Issue title: Proceedings of the San Marino Workshop on Astrophysics and Cosmology for Matter and Antimatter, Italy, September 5–9, 2011

Guest editors: Christian Corda

Article type: Research Article

Authors: Pardy, Miroslav

Affiliations: Department of Physical Electronics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic. E-mail: pamir@physics.muni.cz

Abstract: The Poincaré model of the Lobačevskii geometry is derived from the Fermat principle. The Lobačevskii geometry is interpreted as the Lobačevskii-Fok velocity space geometry of moving particles. The relation of this geometry to the decay of the neutral pi-meson is considered. The generalization of the Lobačevskii geometry is performed and the new angle of parallelism is derived. The light confined circularly in the optical medium is defined as the optical black hole. The existence of the centrifugal force acting on the photon is discussed.

Keywords: The Fermat principle, light ray trajectories, optics, the Poincaré model of the Lobačevskii geometry, Lobačevskii-Fok geometry, generalized Lobačevskii geometry, optical black hole

DOI: 10.3233/JCM-120460

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 13, no. 1-2, pp. 177-188, 2013