Quantization of almost-circular orbits in the Fokker action formalism. General scheme

Abstract: General two-particle system is considered within the formalism of Fokker-type action integrals. It is assumed that the system is invariant with respect to the Aristotle group which is a common subgroup of the Galileo and Poincar\'e groups. It is shown that equations of motion of such system admit circular orbit solutions. The dynamics of perturbations of these solutions is studied. It is described by means of a linear homogeneous set of time-nonlocal equations and is analyzed in terms of eigenfrequencies and eigenmodes. The Hamiltonian description of the system is built in the almost circular orbit approximation. The Aristotle-invariance of the system is exploit to avoid a double count of degrees of freedom and to select physical modes. The quantization procedure and a construction of energy spectrum of the system is proposed.