  A nonlocal and nonlinear theory of hadrons, equivalent to the color singlet
sector two dimensional QCD, is constructed. The phase space space of this
theory is an infinite dimensional Grassmannian. The baryon number of QCD
corresponds to a topological invariant (`virtual rank') of the Grassmannian. It
is shown that the hadron theory has topological solitons corresponding to the
baryons of QCD. ${1\over N_c}$ plays the role of $\hbar$ in this theory; $N_c$
must be an integer for topological reasons. We also describe the quantization
of a toy model with a finite dimensional Grassmannian as the phase space. In an
appendix, we show that the usual Hartree--Fock theory of atomic and condensed
matter physics has a natural formulation in terms of infinite dimensional
Grassmannians.
