Topological Quantization of k-Dimensional Topological Defects and Motion Equations

Abstract

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