Topological quantization of k-dimensional topological defects and motion equations

Using the -mapping method and kth-order topological tensor current theory, we present a unified theory of describing k-dimensional topological defects and obtain their topological quantization and motion equations. It is shown that the inner structure of the topological tensor current is just the dynamic form of the topological defects, which are generated from the zeros of the m-component order parameter vector field. In this dynamic form, the topological defects are topologically quantized naturally and the topological quantum numbers are determined by the Hopf indices and the Brouwer degrees. As the generalization of Nielsen's Lagrangian and Nambu's action for strings, the action and the motion equations of the topological defects are also derived.