A novel strong coupling expansion of the QCD Hamiltonian

TL;DR

This paper introduces a new systematic strong coupling expansion method for the QCD Hamiltonian on a lattice, enabling calculations of vacuum and glueball energies in SU(2) Yang-Mills theory.

Contribution

It presents a novel strong coupling expansion framework for the QCD Hamiltonian using an infinite lattice, incorporating spatial derivatives and enabling perturbative calculations.

Findings

Calculated vacuum energy up to order λ^2.

Determined lowest scalar glueball energy up to order λ^2.

Developed a systematic expansion approach for non-perturbative QCD analysis.

Abstract

Introducing an infinite spatial lattice with box length a, a systematic expansion of the physical QCD Hamiltonian in \lambda = g^{-2/3} can be obtained. The free part is the sum of the Hamiltonians of the quantum mechanics of spatially constant fields for each box, and the interaction terms proportional to \lambda^n contain n discretised spatial derivatives connecting different boxes. As an example, the energy of the vacuum and the lowest scalar glueball is calculated up to order \lambda^2 for the case of SU(2) Yang-Mills theory.