Abstract
Master fields are formulated for finite-$N$ (3+1)-dimensional QCD. They satisfy classical Yang-Mills equations with an infinite number of internal indices and an infinite number of constraints. Master fields and constraints on them in the large-$N$ limit ($N\ensuremath{\rightarrow}\ensuremath{\infty}$ with fixed ${g}^{2}N$) are derived from the finite-$N$ master fields and constraints using vacuum dominance among color-singlet states. Explicit solutions for the large-$N$ constraints are given and used as trial functions in a Hartree-Fock variational calculation. This Hartree-Fock method can include essential features of gluon condensation effects in the QC${\mathrm{D}}_{3+1}$ vacuum which is expected to cause confinement. Inclusion of quark fields and Hartree-Fock equations for the meson energy spectrum are also discussed.
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