Direct evaluation of baryon numbers of empty chiral bags

Goldstone and Jaffe proved using very general arguments that for a chiral bag surrounded by a Skyrme soliton, the baryon number of the Dirac vacuum inside the bag exactly cancels the (known) baryon number of the soliton outside. Their analysis applied to massless quarks. In order to obtain a formalism easier to generalize to massive quarks, we rederive the result for spherical bags by solving the Dirac equations for the inside of the bag and explicitly performing the required summations over the energy levels. (orig.)