Quantum fluctuations and the bag model

We consider a path-integral prescription for quantizing a variation of the bag model of Chodos et al. We treat the bag shape as an independent dynamical variable where associated kinetic terms in the Lagrangian have been taken to zero. We solve exactly a version of the model where a scalar field has a different mass inside and outside the bag. This solution is a free-field theory of a particle with a mass that is the root mean square of the input interior and exterior masses. No remnants of the semiclassical bag structures remain. The fact that the quantum fluctuations have so strongly altered the structure of the theory is associated with the lack of any structure in the surface of the bag. We argue that a surface tension alone is inadequate to control these fluctuations; both a surface tension and a surface thickness are needed