New approach to interactions in the MIT bag

Quark and gluon interactions are computed inside a rigid spherical cavity. The formalism successfully rederives some old MIT bag results for energy shifts and will provide new applications to mixing problems, glue in the ${\eta }^{\prime }$, hadron decays, and gluonium hyperfine splittings. Cavity perturbation theory is shown to be valid if ${\alpha }_s\lesssim 5$ which justifies the MIT group's computations with ${\alpha }_s=2.2\mathrm{}$.