Vibrational modes of massive Skyrmions within the rational map ansatz

In this thesis, we study the vibrational modes of some Skyrmion solutions within the rational map approximation. When the Skyrme field is perturbed around a static solution, the radial and angular vibrations of the field are decoupled; this gives us two sets of eigenvalue equations that provide us the vibrational modes of the solutions when solved. Using the symmetry properties of the solutions of the equation of motion of the model, the conjugate relations among these solutions can be identified. With a physical contraint on the dispersion relation between the mass and the vibration frequency, we obtain an upper bound for the critical pion mass. Finally, we compare between our results with some numerical results obtained by Houghton et al.