Boson Expansion Methods in (1+1)-dimensional Light-Front QCD

TL;DR

This paper derives a bosonic Hamiltonian for (1+1)-dimensional light-front QCD using boson expansion methods, revealing a free meson spectrum in the large N limit.

Contribution

It introduces a boson expansion approach to derive a bosonic Hamiltonian in light-front QCD, connecting bilocal operators to meson states and analyzing the large N limit.

Findings

Bosonic Hamiltonian derived from 2D light-front QCD.

In the large N limit, the theory describes free mesons.

Mass spectrum matches the 't Hooft equation.

Abstract

We derive a bosonic Hamiltonian from two dimensional QCD on the light-front. To obtain the bosonic theory we find that it is useful to apply the boson expansion method which is the standard technique in quantum many-body physics. We introduce bilocal boson operators to represent the gauge-invariant quark bilinears and then local boson operators as the collective states of the bilocal bosons. If we adopt the Holstein-Primakoff type among various representations, we obtain a theory of infinitely many interacting bosons, whose masses are the eigenvalues of the 't Hooft equation. In the large $N$ limit, since the interaction disappears and the bosons are identified with mesons, we obtain a free Hamiltonian with infinite kinds of mesons.