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

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. Its relation to the renormalisation of the coupling constant in the IR is discussed, indicating the absence of infrared fixed points