Bosonization relations as bag boundary conditions

The more sophisticated bag models of hadrons become, the less precisely they seem to determine the bag radius. Idealizing this situation leads to the concept of exact bag models - "Cheshire cat" models (CCM) - where the physics is completely insensitive to changes in the bag radius. CCM are constructed explicitly in 1 + 1 dimensions, where exact bosonization relations are known. In the formalism of bag models, these relations appear as boundary conditions which ensure that the shifting of the bag wall has no physical effect. Other notable features of (1 + 1)-dimensional CCM are: (i) fermion number, though classically confined, can escape the bag via a vector current anomaly at the surface; (ii) essentially the same boundary action works for a variety of models and its symmetries determine those of the external boson fields. Remarkably enough, this (1 + 1)-dimensional boundary action has precisely the same form as the one used in (3 + 1)-dimensional chiral bag models, lending support to the belief that the latter are indeed approximate CCM. These (1 + 1)-dimensional results are expected to provide useful guidelines in the attempt to, at least approximately, bosonize (3 + 1)-dimensional QCD.