Formulating Light Cone QCD on the Lattice

TL;DR

This paper develops a lattice QCD Hamiltonian near the light cone, deriving an effective quadratic Hamiltonian and approximating the ground state wave functional as the system approaches the light cone.

Contribution

It introduces a parameter-dependent Hamiltonian for lattice QCD near the light cone and derives an effective quadratic form solvable by standard methods.

Findings

Effective Hamiltonian $H_{eff}$ derived for near light cone QCD

Ground state wave functional approximated variationally as $ o 0$

Framework facilitates studying QCD in light cone limit

Abstract

We present the near light cone Hamiltonian $H$ in lattice QCD depending on the parameter $\eta$, which gives the distance to the light cone. Since the vacuum has zero momentum we can derive an effective Hamiltonian $H_{eff}$ from $H$ which is only quadratic in the momenta and therefore solvable by standard methods. An approximate ground state wave functional is determined variationally in the limit $\eta \to 0$.