An Approximated Analytical Solution For Classical Skyrme Model

Quantum Chromodynamics(QCD)was believed to be the fundamental the-ory of the strong interaction,which describes the interaction of quarks and glu-ons.Unfortunately,calculating the properties of hadrons from the QCD lagrangian has proven to be a very difficult task due to its strongly coupled nonlinear theory in low energy region.Although we have made great progress in understanding strong interaction especially in the ultraviolet region, properties of medium and low energy QCD still present challenges to particle physicist and remain to be understood. The Skyrme model is nowa-days one of the strongest candidates for a description of the low-energy regime of QCD. Developed in the beginning of the 60's by T.H.R. Skyrme, it consists of a nonlinear theory of mesons where its main feature is the presence of topological solitons as solutions. Each of these solutions is associated with a conserved topological charge, the winding number, which Skyrme interpreted as the baryon number.In other areas of physics Skyrme model also play a very important role, such as Nuclear physics, astrophysics, condensed matter physics, etc.ChapterⅠ:First to describe the basic theory of strongly interacting QCD and its basic characteristics are introduced, Then, this paper expounds the QCD low-energy theory and equivalent model. The QCD low-energy theory, which has proven to be reasonably successful, including QCD sum rule, lattice QCD, large-Nc QCD and chiral perturbation theory(CHPT) etc., this paper CHPT are introduced in detail. Because of the direct use QCD solving bound states hadron have great difficulty, in one hand, people developing some such as above mentioned QCD low-energy theory. On the other hand developing the phenomenological model with the QCD basis, such as the quark potential model, the Bag model, the solitary particle model, etc.ChapterⅡ:Because large-Nc QCD and the nonlinear sigma model has very close relation with the Skyrme model,so,first we made a brief introduction about them. Sec-ondly,the Skyrme model with massless is studied in detail. An approximate analytical solution is proposed for the model,in a good agreement with that given by the exact numeric solution.In order to check the solution further, the static properties of nucleons is then computed. The comparisons with the previous results as well as the experimen-tal values are also presented.Finally, numerical methods used for solving equations are discussed.ChapterⅢ:Firstly,rational maps and multi-baryon Skyrmion states are introduced in simple. Then, the Skyrme model with mass is studied in detail. An approximate analytical solution is also proposed for the model,in a good agreement with that given by the exact numeric solution.But with the above approximate analytical solution different is that here the solution only one form when baryon number B,πmeson mass parameter m change. And the second chapter similarly, we calculated the static properties of nucleons and some Related numerical methods especially super relaxation method are discussed.Finally, in the fifth chapter of this paper, we summarize the main results and give an outlook of the future in this field.