  The dressing of bare massless quarks is described with a spatial theory based
on the self-consistent solution of the QCD field equations. After quantization
these equations are expressed in terms of quark and gluon creation and
annihilation operators and admit a surprisingly elegant exact (operator)
solution which eliminates any multi-quark admixtures in the state vector.
Hence, this theory is uniquely and exclusively suited to describe the dressing
of single bare quarks. After factorizing out the operators, a finite set of
coupled non-linear differential equations results for the reduced c-number
quark and gluon fields. These yield three distinct solitonlike solutions,
corresponding to the three observed quark generations. Physically each solution
represents a quark absolutely confined by the gluon potentials it generates.
The radii of the three generations are given by (2.0428..., 1 , 1)/E, while the
binding energies are linked to the SU(3) structure constants and given by E -
(32/9, 16/9, 1)E, where E sets the energy scale of the system. To stabilize the
system general relativity is required, putting E in the Planck domain. After
the introduction of a vacuum term characterized by the cosmological constant
the dressed quark mass can be expressed in terms of the gravitational and
cosmological constant, nevertheless lying in the MeV range. After the inclusion
of the other gauge interactions this theory might well serve as a theoretical
laboratory for quantitative tests of the unification of general relativity and
QFT in a constrained Planck scale environment.
