Exact self-energy for cavity pair theory

Wentzel pair theory is examined for a massless scalar field which interacts with a highly localized spherically symmetric source while confined to a spherical cavity of radius R. The ground-state energy, interpreted as the self-energy of the source, is determined exactly as a function of a dimensionless renormalized coupling constant α. In the limit of a point source, the renormalized self-energy is given as E = A/R, where A is a nonanalytic function of α. The first two orders of perturbation theory give A = 0.131(α-α2). For α = 0.5, first-order perturbation theory gives a result which is 45% above the exact value, while inclusion of corrections through second order in α gives a result which is 27% below the exact value. The model suggests that the perturbation expansion for radiative corrections in intermediate-coupling cavity field theories such as cavity QCD may be unreliable