Dyson--Schwinger approach to Hamiltonian Quantum Chromodynamics

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.

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• Higher order heavy quark Green's functions in Coulomb gauge
• Three-quark confinement potential from the Faddeev equation

Cited by in corpus (8)

• Improved variational approach to QCD in Coulomb gauge
• Covariant variational approach to Yang-Mills Theory: Thermodynamics
• Variational and Dyson--Schwinger Equations of Hamiltonian Quantum Chromodynamics
• Schwinger-Dyson Equations in Coulomb Gauge Consistent with Numerical Simulation
• The Equal-Time Quark Propagator in Coulomb Gauge
• Dynamical Quark Mass Generation in QCD\textsubscript{3} within the Hamiltonian approach in Coulomb gauge
• Dyson--Schwinger Approach to Hamiltonian QCD
• Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions