Vacuum and excited states of Coulomb-gauge SU(n) Yang-Mills fields

Properties of the quantized SU(n) Yang-Mills fields, for n=2, 3, and 4, have been studied numerically. We apply the Hamiltonian formalism to the continuum theory, with a truncated momentum expansion in a finite volume, and have examined states in the vacuum sector using variational methods in the Coulomb gauge. The results depend on the strength of the interaction constant α, with a transition at nα∼1. For small α, there is a gap between excited-state energies and the vacuum energy, but the excited $0^{++}$ states correspond to pairs of weakly interacting transverse gluons. For larger α, the excited states are associated with a collective degree of freedom and can be identified with a glueball. There is no evidence for the existence of an instability associated with magnetic interactions.