Quantization of almost-circular orbits in the Fokker action formalism

Abstract

A relativistic quark model of mesons formulated within the formalism of Fokker-type action integrals is proposed, in which an interquark interaction is mediated by scalar-vector superposition of higher derivative fields. In the non-relativistic limit the model describes a two-particle system with the linear potential. In order to analyze the model in the essentially relativistic domain the perturbed circular orbit approximation and certain principle of selection of physically meaningful solutions are applied which permit one to perform the canonical quantization of the model. It is shown that the model reproduces well specific features of the light meson spectroscopy. * duviryak@icmp.lviv.ua

Regge trajectories in the framework of the relativistic action-at-a-distance theory

“…Used here is the almost-circular-orbit (ACO) approximation scheme developed in the previous work of the author [56]. The scheme is based on the fact that all known in the literature two-particle Fokker-type systems with the attractive (in some meaning) interaction possess exact solutions of the shape of concentric planar circular particle orbits of radii R a (Ω) dependent on an angular velocity Ω; see [59][60][61].…”

“…The scheme is based on the fact that all known in the literature two-particle Fokker-type systems with the attractive (in some meaning) interaction possess exact solutions of the shape of concentric planar circular particle orbits of radii R a (Ω) dependent on an angular velocity Ω; see [59][60][61]. In [56] this is proven for a general two-particle Fokker-type system,…”

“…Let us consider a circular-orbit solution of the Rivacoba-Weiss model. Using the action (2.1), (2.8) for a system of two particles of equal masses m a ≡ m (a = 1, 2) and following the general methodology proposed in [61] or [56], one states a relation between the angular velocity Ω of circulating particles and the radius R of their orbits. It is convenient, instead of R, to work with particle velocities v a ≡ v = RΩ.…”

“…In order to study the system in ACO approximation we need to construct the reduced 2×2 dynamical matrix D ⊥ [56] and then to calculate the frequency ω r of radial oscillations or, equivalently, the fraction λ = ω r /Ω, as a function of either Ω, J, v or (which is most convenient) φ. This is done in Appendix A.…”

“…Recently, a quantization method of two-particle Fokker-type (i.e., time-nonlocal) systems in an almostcircular-orbit (ACO) approximation has been proposed by the author [56]. The method is appropriate for strongly coupled systems.…”