Operatorial quantization of the Born-Infeld Skyrmion model and hidden symmetries

The SU(2) collective coordinates expansion of the Born-Infeld Skyrmion Lagrangian is performed. The classical Hamiltonian is computed from this special Lagrangian in an approximative way: it is derived from the expansion of this non-polynomial Lagrangian up to second-order variable in the collective coordinates. This second-class constrained model is quantized by the Dirac Hamiltonian method and symplectic formalism. Although it is not expected to find symmetries on second-class systems, a hidden symmetry is disclosed by formulating the Born-Infeld Skyrmion model as a gauge theory. To this end we developed a new constraint conversion technique based on the symplectic formalism. Finally, a discussion on the role played by the hidden symmetry on the computation of the energy spectrum is presented.