Expansion in the width and collective dynamics of a domain wall

We show that collective dynamics of a curved domain wall in a (3+1)-dimensional relativistic scalar field model is represented by a Nambu-Goto membrane and (2+1)-dimensional scalar fields defined on the world-sheet of the membrane. Our argument is based on a recently by us proposed version of the expansion in the width. The derivation of the expansion is significantly reformulated for the present purpose. Third- and fourth-order corrections to the domain wall solution are considered. We also derive an equation of motion for the core of the domain wall. Without the (2+1)-dimensional scalar fields this equation would be non-local. (orig.)