摘要
In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.
基金
The project supported by National Natural Science Foundation of China under Grant No. 10475034 and the Doctor Education Fund of the Educational Department of China.Acknowledgments It is a great pleasure to thank Dr. Y.X. Liu and Dr. Z.G. Huang for many useful discussions.
