Dyson--Schwinger approach to Hamiltonian Quantum Chromodynamics

TL;DR

This paper extends a Hamiltonian approach using Dyson--Schwinger equations to full QCD, incorporating quark-gluon interactions in a variational framework to analyze the QCD vacuum state.

Contribution

It generalizes a method for non-Gaussian wave functionals from Yang--Mills theory to full QCD, including explicit quark-gluon couplings and deriving equations of motion for variational kernels.

Findings

Derived Dyson--Schwinger equations for QCD variational kernels.

Expressed n-point functions in terms of variational parameters.

Established a framework for energy minimization in QCD vacuum analysis.

Abstract

The general method for treating non-Gaussian wave functionals in the Hamiltonian formulation of a quantum field theory, which was previously proposed and developed for Yang--Mills theory in Coulomb gauge, is generalized to full QCD. For this purpose the quark part of the QCD vacuum wave functional is expressed in the basis of coherent fermion states, which are defined in term of Grassmann variables. Our variational ansatz for the QCD vacuum wave functional is assumed to be given by exponentials of polynomials in the occurring fields and, furthermore, contains an explicit coupling of the quarks to the gluons. Exploiting Dyson--Schwinger equation techniques, we express the various $n$-point functions, which are required for the expectation values of observables like the Hamiltonian, in terms of the variational kernels of our trial ansatz. Finally the equations of motion for these variational kernels are derived by minimizing the energy density.