Method of collective degrees of freedom in spin-coherent-state path integral

We present a detailed field-theoretical description of those collective degrees of freedom (CDF) which are relevant to study macroscopic quantum dynamics of a quasi-one-dimensional ferromagnetic domain wall. We apply the spin-coherent-state path integral in the proper discrete time formalism (a) to extract the relevant CDFs, namely, the center position and the chirality of the domain wall, which originate from the translation and the rotation invariances of the system in question, and (b) to derive an effective action for the CDFs by elimination of environmental zero modes with the help of the Faddeev-Popov technique. The resulting effective action turns out to be such that both the center position and the chirality can be formally described by a boson-coherent-state path integral. However, this is only formal; there is a subtle departure from the latter