Effective hamiltonians for 1/N expansion in two-dimensional QCD

Abstract

We discuss the general structure of effective hamiltonians for systematic 1/N expansion in QCD using the light-cone quantization. These are second-quantized hamiltonians acting on the Fock space of mesons and glueballs defined by the solution of the $N=\infty$ problem. In the two-dimensional case we find only cubic and quartic interaction terms, and give explicit expressions for the vertex functions as integrals of solutions of 't Hooft equation. As examples of possible applications of our formalism, we study 1/N corrections to meson mass and form factors for decays of $Q\bar{q}$ states, recently discussed by Grinstein and Mende in the large-N limit. We find that 1/N is a good small expansion parameter.