Abstract
We present a concrete model of a low energy effective field theory of QCD, the well-known Skyrme Model. Specifically, we will work with the BPS submodel in order to describe the binding energies of nuclei. This BPS Skyrme model is characterized by having a saturated bound for the energy proportional to the baryon number of the nuclei. After presenting this classical result, we will proceed with a semi-classical quantization of the coordinates of spin and isospin. Then, with the further inclusion of the Coulomb interaction as well as a small explicit breaking of the isospin symmetry, we finally calculate the binding energies of nuclei, where an excellent agreement has been found for the nuclei with high baryon number. Besides this, we also apply this model to the study of some thermodynamic properties and to neutron stars.
Highlights
Skyrme proposed an effective theory for the description of the low-energy limit of strong interactions where the primary fields are mesons [1, 2]. This novel idea is what nowadays we call Skyrme Model and it was supported when in the large Nc limit of QCD it was found that an effective theory of mesons arises [3]
Nuclei appear as collective excitations of these fundamental degrees of freedom and are characterized by a topological charge which is identified with the baryon number, ensuring in this way its conservation
(1 + |u|2)−2dξdudu = (1 + |u|2)−2dξudu. This symmetry is a subgroup of the full volumepreserving diffeomorphism (VPD) corresponding to the sextic term, it is the potential term depending on ξ what breaks it
Summary
Asking the Lagrangian to be no more than quadratic in time derivatives, so a standard hamiltonian formulation is possible, these L6 and L0 are the only extra terms allowed, and the generalized Skyrme Model is. The idea of this generalization resolves a problem of the Standard Skyrme model, where the binding energies we get from it are too large.
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