Eur. Phys. J. Plus (2014) 129: 267
https://doi.org/10.1140/epjp/i2014-14267-y

Regular Article

Quantization of almost-circular orbits in the Fokker action formalism

Institute for Condensed Matter Physics of NAS of Ukraine, 1 Svientsitskii Street, UA-79011, Lviv, Ukraine

^* e-mail: duviryak@icmp.lviv.ua

Received: 3 June 2014
Revised: 24 October 2014
Accepted: 15 November 2014
Published online: 16 December 2014

Abstract

The time-non-local action principle of Fokker type determining a two-particle dynamics is considered. The system is assumed to be general but invariant with respect to the Aristotle group, which is a common subgroup of the Galileo and Poincaré groups. It is shown that integral-differential equations of motion of such system admit circular orbit solutions. The dynamics of perturbations of these solutions is derived and studied. On this ground, the Hamiltonian description of the time-non-local two-particle system is built in the almost circular orbit approximation. The Aristotle invariance of the system is exploited to select physical degrees of freedom. The quantization procedure and a construction of energy spectrum of the system is proposed. The application in meson spectroscopy is meant.