  The interaction between an atom and the quantized electromagnetic field
depends on the position of the atom. Then the atom experiences a force which is
the minus gradient of this interaction. Through the Heisenberg equations of
motion and the Born-Markov approximation, the mean and correlation of the force
are obtained, showing that the center-of-mass motion of the atom is damped and
diffused. This approach can be easily generalized to multi-level atoms, where
the damping force and diffusion coefficients are just the weighted average of
the contributions from all pairs of energy levels that have nonvanishing dipole
elements. It is shown that these results are invariant under Galilean
transformation, and in principle can be used to determine the velocity of the
lab relative to the background radiation.
