  Using approximate methods of nonperturbative quantization \`a la Heisenberg
and taking into account the interaction of gauge fields with quarks, we find
regular solutions describing the following configurations: (i) a spinball
consisting of two virtual quarks with opposite spins; (ii) a quantum monopole;
(iii) a spinball-plus-quantum-monopole system; and (iv) a
spinball-plus-quantum-dyon system. A comparison with quasi-particles obtained
by lattice and phenomenological analytical calculations is carried out. All
these objects (except the spinball) are embedded in a bag created by the
quantum coset condensate consisting of the SU(3)/(SU(2)~$\times$~U(1)) gauge
fields. The existence of these objects is due to the Meissner effect, which
implies that the SU(2)~$\times$~U(1) gauge fields are expelled from the
condensate. The physical interpretation of these solutions is proposed in two
different forms: (i) an approximate glueball model; and (ii) quantum
fluctuations in the coset condensate of the nonperturbative vacuum or in a
quark-gluon plasma. For the spinball and the spinball-plus-quantum-monopole
configuration, we obtain energy spectra, in which mass gaps are present. The
process of deconfinement is discussed qualitatively. It is shown that the
quantum chromodynamics constant $\Lambda_{\text{QCD}}$ appears in the
nonperturbative quantization \`a la Heisenberg as some constant controlling the
correlation length of quantum fields in a spacelike direction.
