Quark-Quark Forces in Quantum Chromodynamics

TL;DR

This paper derives analytical expressions for quark-quark interactions in QCD using Bethe-Salpeter formalism, investigates infrared effects, and reveals how the interaction character changes from discrete to continuous spectra, suggesting a quasicrystal vacuum structure.

Contribution

It provides a relativistic, single-time reduction approach to quark interactions in QCD, highlighting the energy dependence and spectrum transition effects.

Findings

Analytical quasipotential expressions for quark-quark interactions in QCD.

Infrared singularities influence the force character in QCD.

Interaction quasipotential oscillates in the continuous spectrum, indicating a quasicrystal vacuum.

Abstract

By single-time reduction technique of Bethe-Salpeter formalism for two-fermion systems analytical expressions for the quasipotential of quark-quark interactions in QCD have been obtained in one-gluon exchange approximation. The influence of infrared singularities of gluon Green`s functions on the character of quark-quark forces in QCD has been investigated. The way the asymptotic freedom manifests itself in terms of two-quark interaction quasipotential in quantum chromodynamics is shown. Consistent relativistic consideration of quark interaction problem by single-time reduction technique in QFT allows one to establish a nontrivial energy dependence of the two-quark interaction quasipotential. As a result of the energy dependence of the interaction quasipotential, the character of the forces changes qualitatively during the transition from the discrete spectrum (the region of the negative values of the binding energy) to the continuous spectrum (that of the positive values of the binding energy): the smooth behaviour of the interaction quasipotential in the discrete spectrum goes into the oscillation in the continuous spectrum. This result gives a visual physical picture where the oscillations may be interpreted as a manifestation of a quasicrystall structure of the vacuum.