Meson wave functions in two-dimensional quantum chromodynamics

Abstract

We consider 't Hooft's eigenvalue problem for the meson spectrum in two-dimensional quantum chromodynamics by defining some alternative formulations whose equivalence we prove. Hence we are able to prove that the spectrum is discrete and of finite multiplicity and to derive bounds (upper and lower) for the eigenvalues (ground state, $n\mathrm{th}$ state, and $n\ensuremath{\rightarrow}\ensuremath{\infty}$ state). We prove that the functions are analytic and use this to carry out explicit numerical calculations of the wave functions for various values of the quark masses and to recalculate the meson spectrum.