SU(2)Chern-Simons涡旋解的拓扑结构

Topological Structure of SU(2) Chern-Simons Vortices

运用规范势分解理论研究了Dunne-Jackiw-Pi-Trugenberger模型中的自对偶方程,得到一个静态的自对偶Chern-Simons多涡旋解,每个涡旋由5个参数描述。发现了自对偶解与拓扑数之间的关系,而拓扑数由Brouwer度与Hopf指标确定。同时,也研究了该涡旋解的磁通量的拓扑量子化。

The self-dual equation and its solution in SU（2） Dunne-Jackiw-Pi-Trugenberger model has been discussed with special ansatz for the Lie algebraic structures of su（2） and gauge potential decomposition. We Obtained a new concrete self-dual equation and found the relationship between SU （2） Chern-Simons vortices and topological number which is determined by Hopf indices and Brouwer degrees of φ-mapping. M-vortices solutions are discribed by using 5m parameters （two positions, one scale, one phase per vortex and one charge of each vortex）. The quantization of flux is also studied in this case.