Dyson--Schwinger Approach to Hamiltonian QCD

TL;DR

This paper applies Dyson--Schwinger equations within the Hamiltonian framework of QCD to perform variational calculations using non-Gaussian wave functionals, deriving and numerically solving equations for variational kernels.

Contribution

It introduces a method to express n-point functions via Dyson--Schwinger equations in Hamiltonian QCD and solves the resulting equations numerically.

Findings

Derived equations of motion for variational kernels.

Expressed n-point functions in terms of variational kernels.

Numerically solved the equations for specific kernels.

Abstract

Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By means of the DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the variational kernels of our trial ansatz. Equations of motion for these variational kernels are derived by minimizing the energy density and solved numerically.