Discretized light-cone quantization and the effective interaction in hadrons

TL;DR

This paper introduces a non-perturbative, Hamiltonian-based discretized light-cone quantization method for calculating hadron spectra and wavefunctions directly from QCD, avoiding divergences through renormalization.

Contribution

It develops a comprehensive Hamiltonian approach to discretized light-cone quantization, deriving an effective interaction and solving for meson spectra from first principles.

Findings

Derived a regularized effective interaction for QCD

Obtained meson mass spectrum and wavefunctions

Developed an almost solvable integral equation for mesons

Abstract

Light-cone quantization of gauge theories is discussed from two perspectives: as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and as a novel method for simulating quantum field theory on a computer. A general non-perturbative method for numerically solving quantum field theories, `discretized light-cone quantization', is outlined. Both the bound-state spectrum and the corresponding relativistic wavefunctions can be obtained by matrix diagonalization and related techniques. Emphasis is put on the construction of the light-cone Fock basis and on how to reduce the many-body problem to an effective Hamiltonian. The usual divergences are avoided by cut-offs and subsequently removed by the renormalization group. For the first time, this programme is carried out within a Hamiltonian approach, from the beginning to the end. Starting with the QCD-Lagrangian, a regularized effective interaction is derived and renormalized, ending up with an almost solvable integral equation.Its eigenvalues yield the mass spectrum of physical mesons, its eigenfunctions yield their wavefunctions including the higher Fock-space components. An approximate but analytic mass formula is derived for all physical mesons.