Quantum Hadrondynamics in Two Dimensions

Abstract

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.