  An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe
the dynamics of inhomogeneous magnetization in a current-carrying wire. The
coefficients of all the terms in this equation are calculated
quantum-mechanically for a simple model which includes impurity scattering.
This is done by comparing the energies and lifetimes of a spin wave calculated
from the LLG equation and from the explicit model. Two terms are of particular
importance since they describe non-adiabatic spin-transfer torque and damping
processes which do not rely on spin-orbit coupling. It is shown that these
terms may have a significant influence on the velocity of a current-driven
domain wall and they become dominant in the case of a narrow wall.
