Duan's Topological Current Theory, Duan-Ge's U(1) Gauge Potential Decomposition Theory And Their Applications In Neutron Star

In this dissertation,by using of Duan's topological current theory and Duan-Ge U(1) gauge potential decomposition theory proposed by Prof.Duan Yi-Shi and Prof.Ge Mo-Lin,we have studied a two component superfluid Bose condensed system,which is believed to be realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonic superconductor. We propose that this system possesses two kinds of topological defects: vortex lines and monopoles.Firstly,we give an introduction of Duan's topological current theory and Duan-Ge U(1) gauge potential decomposition theory.The basic theory of neutron stars is also introduced.Secondly,by making use of Duan's topological current theory and Duan-Ge U(1) gauge potential decomposition theory,we discuss the free energy density of the two component superfluid Bose condensed system.The inner topological structures of fields are characterized by theφ-mapping topological numbers-the Hopf indices and Brouwer degrees.In this two component superfluid Bose condensed system,we point out that there exist two kinds of knotted solitons, described by BF action and Hopf invariant.These actions are just the total sum of all the self-linking and linking numbers of knot family.Finally,we research the magnetic field of this two component Bose condensed system in detail and come to the conclusion:beside the knotted vortices, another kind of topological defects,namely the magnetic monopoles,also possibly exist in this system.Furthermore,in light of Duan's topological current theory and Duan-Ge U(1) gauge potential decomposition theory,the monopoles current density is expressed asδ((?)) and the topological charges are characterized by theφ-mapping topological numbers-the Hopf indices and the Brouwer degrees.Moreover,these monopoles are located at the zero points of the fieldφand the branch processes during the evolution are also dicussed.