A self-consistent dynamical bag model

In this thesis we investigate the bag models of hadrons with dynamical boundaries. Unlike the few previous works, which focused mainly on the phenomenology, here we examine the issue of the consistency of dynamical bag models and we study the exact dynamics of the fields coupled to the boundary motion.; We first study the effects of the boundary motion in two simple systems: the Schrödinger equation in a cavity with sinusoidally varying radius and a scalar field in a spherical cavity whose boundary moves self-consistently under the field's pressure and a static potential. We find the occurrence of boundary-driven resonances in both systems and the self-focusing of the energy for the system with self-consistent motion of the boundary [15, 16].; Applying the null-lines method to the equations of motion derived from the MIT bag Lagrangian with massless quarks and a spherical moving boundary, we prove that they admit only one solution, which corresponds to a bag expanding at the speed of light and we present the analytical solution [17]. With the same method we then find the self-consistent classical solutions of a spherically symmetric chiral bag in which the motion of the bag surface is determined by the conservation of the total energy. Remarkably we find that when the bag interacts with an external pion wave with frequency ν three different kinds of resonances can occur: fermionic for ν ≃ E_n − E_k, geometric for ≃ nπ/R₀, and σ-resonances for ν ≃ (2n + 1)π/(2 R₀). We explain how the σ-resonances may be related to the Roper resonance [18].