Operatorial quantization of Born-Infeld Skyrmion model and hidden symmetries

TL;DR

This paper quantizes the Born-Infeld Skyrmion model using operator methods, reveals hidden symmetries by reformulating it as a gauge theory, and discusses their impact on the energy spectrum.

Contribution

It introduces a new constraint conversion technique within the symplectic formalism to uncover hidden symmetries in a second-class constrained model.

Findings

Hidden gauge symmetry is identified in the Born-Infeld Skyrmion model.

The quantization reveals the role of hidden symmetry in energy spectrum calculations.

A novel method for converting constraints in symplectic formalism is proposed.

Abstract

The SU(2) collective coordinates expansion of the Born-Infeld\break Skyrmion Lagrangian is performed. The classical Hamiltonian is computed from this special Lagrangian in 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 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.