<正> 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 φ-mapping topological current theory,we investigate the ...<正> 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 φ-mapping topological current theory,we investigate the topological struc-ture of the vortex lines in LCs in detail.A topological invariant,i.e.,the Chern-Simons(CS)action for the knottedvortex lines is presented,and the CS action is shown to be the total sum of all the self-linking and linking numbers ofthe knot family.Moreover,it is pointed out that the CS action is preserved in the branch processes of the knotted vortexlines.展开更多
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.
文摘<正> 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 φ-mapping topological current theory,we investigate the topological struc-ture of the vortex lines in LCs in detail.A topological invariant,i.e.,the Chern-Simons(CS)action for the knottedvortex lines is presented,and the CS action is shown to be the total sum of all the self-linking and linking numbers ofthe knot family.Moreover,it is pointed out that the CS action is preserved in the branch processes of the knotted vortexlines.
