Method of Collective Degrees of Freedom in Spin Coherent State Path Integral

Abstract

We present a detailed field theoretic 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 spin coherent state path integral (SCSPI) in the proper discrete time formalism (a) to extract the relevant CDF's, 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 effective action for the CDF's by elimination of environmental zero-modes with the help of the {\it 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 boson coherent state path integral. However, this is only formal; there is a subtle departure from the latter.