A nonlocal and nonlinear theory of hadrons, equivalent to the color singlet sector of two-dimensional QCD, is constructed. The phase 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. [Formula: see text] plays the role of ħ 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.