  The infrared behavior of perturbative quantum gravity is studied using the
method developed for QED by Faddeev and Kulish. The operator describing the
asymptotic dynamics is derived and used to construct an IR-finite S matrix and
space of asymptotic states. All-orders cancellation of IR divergences is shown
explicitly at the level of matrix elements for the example case of
gravitational potential scattering. As a practical application of the
formalism, the soft part of a scalar scattering amplitude is related to the
gravitational Wilson line and computed to all orders.
