Abstract
We investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD. We use a non-Gaussian vacuum wave functional which includes the coupling of the quarks to the spatial gluons. The expectation value of the QCD Hamiltonian is expressed by the variational kernels of the vacuum wave functional by using the canonical recursive Dyson--Schwinger equations (CRDSEs) derived previously. Assuming the Gribov formula for the gluon energy we solve the CRDSE for the quark propagator in the bare-vertex approximation together with the variational equations of the quark sector. Within our approximation the quark propagator is fairly insensitive to the coupling to the spatial gluons and its infrared behaviour is exclusively determined by the strongly infrared diverging instantaneous colour Coulomb potential.
Highlights
Confinement and the spontaneous breaking of chiral symmetry leading to the dynamical generation of a constituent quark mass are the most important low-energy phenomena of quantum chromodynamics (QCD) at ordinary density and temperature
Much progress has been made in recent years using functional continuum methods like Dyson-Schwinger equations (DSEs) [1,3,4], functional renormalization group (FRG) flow equations [2,5], or variational methods in the Hamiltonian [18,19,24,25,26,27,28,29,30,31,32,33] or Lagrange [34,35] form
In the Appendix we present the details of the infrared analysis of the relevant canonical recursive Dyson-Schwinger equations (CRDSEs)
Summary
Confinement and the spontaneous breaking of chiral symmetry leading to the dynamical generation of a constituent quark mass are the most important low-energy phenomena of quantum chromodynamics (QCD) at ordinary density and temperature Research on this subject has been ongoing for decades The upshot is a set of DSE-like equations (named canonical recursive Dyson-Schwinger equations, CRDSEs) which relate the various n-point functions of the quark and gluon fields to the variational kernels of the vacuum wave functional. In the Appendix we present the details of the infrared analysis of the relevant CRDSEs
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