Quantum Hadrondynamics in Two Dimensions

TL;DR

This paper develops a nonlocal, nonlinear two-dimensional QCD model of hadrons using infinite-dimensional Grassmannians, revealing topological solitons as baryons and connecting quantum properties to topological invariants.

Contribution

It introduces a novel Grassmannian-based framework for 2D QCD, linking baryon number to topological invariants and exploring soliton solutions.

Findings

Topological solitons correspond to baryons in the model.

Baryon number is a topological invariant ('virtual rank') of the Grassmannian.

Quantization relates 1/Nc to Planck's constant.

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.