The QCD String with Quarks. II. Light Cone Hamiltonian

TL;DR

This paper derives a light-cone Hamiltonian for a quark-antiquark system incorporating confinement, explores various dynamical regimes, and connects it to known 1+1 QCD results, advancing understanding of QCD string dynamics.

Contribution

It introduces a novel light-cone Hamiltonian for the QCD string with quarks, including confinement effects and different dynamical regimes, linking to established 1+1 QCD models.

Findings

Derived a gauge-invariant light-cone Hamiltonian with confinement.

Identified limiting regimes including the 1+1 QCD case.

Discussed the role of the light-cone string in energy-momentum contributions.

Abstract

The light-cone Hamiltonian is derived from the general gauge -- and Lorentz -- invariant expression for the $q\bar{q}$ Green's function, containing confinement via the area law for the Wilson loop.The resulting Hamiltonian contains in a nonadditive way contributions from quark and string degrees of freedom. Different limiting dynamical regimes of the system of quarks connected by the string are found. In the limit of no transverse motion one recovers the t'Hooft's 1+1 QCD Hamiltonian. The correspondence with the rest frame Hamiltonian spectrum is established. The important notion of the light-cone string, contributing significantly to the energy--momentum is discussed.