The Classical Relativistic Quark Model in the Rest-Frame Wigner-Covariant Coulomb Gauge

TL;DR

This paper reformulates a classical scalar quark model within a covariant Hamiltonian framework, deriving equations of motion and exploring color confinement and asymptotic freedom in a relativistic setting.

Contribution

It introduces a Wigner-covariant rest-frame formulation of the classical scalar quark model with explicit Hamiltonian dynamics and color singlet constraints.

Findings

Derivation of second order equations of motion for the color field and particles.

Identification of a pseudoclassical asymptotic freedom mechanism.

Regularization of quark self-energy through color singlet constraints.

Abstract

The system of N scalar particles with Grassmann-valued color charges plus the color SU(3) Yang-Mills field is reformulated on spacelike hypersurfaces. The Dirac observables are found and the physical invariant mass of the system in the Wigner-covariant rest-frame instant form of dynamics (covariant Coulomb gauge) is given. From the reduced Hamilton equations we extract the second order equations of motion both for the reduced transverse color field and the particles. Then, we study this relativistic scalar quark model, deduced from the classical QCD Lagrangian and with the color field present, in the N=2 (meson) case. A special form of the requirement of having only color singlets, suited for a field-independent quark model, produces a ``pseudoclassical asymptotic freedom" and a regularization of the quark self-energy.