| Ⅰ.Introduction and preliminaries | 第7-18页 |
| 1.1 Purpose and outline | 第8-9页 |
| 1.2 The multi magnetic monopoles | 第9-13页 |
| 1.3 The φ-mapping theory | 第13-18页 |
| Ⅱ.Foundation of the φ-mapping topological current theory(generalized function) | 第18-37页 |
| 2.1 Introduction | 第18-23页 |
| 2.2 Generalized Heviside theorem | 第23-27页 |
| 2.3 The φ-mapping topological current density | 第27-32页 |
| 2.4 The φ-mapping topological current | 第32-34页 |
| 2.5 Hopf-Poincaré theorem and Morse theory | 第34-37页 |
| Ⅲ.Topological current theory of defects | 第37-61页 |
| 3.1 Introduction | 第37-39页 |
| 3.2 Topological current theory of defects | 第39-43页 |
| 3.3 Bifurcation prosesses of defects | 第43-48页 |
| 3.4 Defect structure in time-dependent Ginzburg-Landau model | 第48-54页 |
| 3.5 Instability and evolution of defects in TDGL model | 第54-61页 |
| Ⅳ.The φ-mapping topological field theory and its applications | 第61-89页 |
| 4.1 Introduction | 第61-63页 |
| 4.2 Decomposition of the gauge potential | 第63-66页 |
| 4.3 The φ-mapping topological field theory of vector field | 第66-69页 |
| 4.4 Abelian structure of Yang-Mills theory | 第69-74页 |
| 4.5 Topological field theory of spinor field | 第74-83页 |
| 4.6 Integer and half-integer quantization conditions in quantum mechanics | 第83-89页 |
| Ⅴ.Effective gauge dynamics of the Bose-Einstein condensate | 第89-107页 |
| 5.1 Introduction | 第89-90页 |
| 5.2 Linearized Gross-Pitaevskii equation | 第90-93页 |
| 5.3 Ground state of trapped BEC | 第93-96页 |
| 5.4 The quantized vortices in Bose condensate | 第96-99页 |
| 5.5 Circulation condition for two-component Bose condensate | 第99-107页 |
| Ⅵ.Conclusion | 第107-109页 |
| Bibliography | 第109-116页 |
| Publication | 第116-117页 |
| 致谢 | 第117页 |
