Expansion of the Yang-Mills Hamiltonian in spatial derivatives and glueball spectrum

Understand

A strong coupling expansion of the SU(2) Yang-Mills quantum Hamiltonian is carried out in the form of an expansion in the number of spatial derivatives, using the symmetric gauge \epsilon_{ijk} A_{jk}=0.

• Introducing an infinite lattice with box length a, I obtain a systematic strong coupling expansion of the Hamiltonian in \lambda\equiv g^{-2/3}, with the free part being the sum of Hamiltonians of Yang-Mills quantum mechanics of constant fields for each box, and interaction terms of higher and higher number of spatial derivatives connecting different boxes.
• The corresponding deviation from the free glueball spectrum, obtained earlier for the case of the Yang-Mills quantum mechanics of spatially constant fields, is calculated using perturbation theory in \lambda.
• As a first step, the interacting glueball vacuum and the energy spectrum of the interacting spin-0 glueball are obtained to order \lambda^2.