  We develop a unified framework for the construction of soft dressings at
boundaries of spacetime, such as the null infinity of Minkowski spacetime and
the horizon of a Schwarzschild black hole. The construction is based on an old
proposal of Mandelstam for quantizing QED and considers matter fields dressed
by Wilson lines. Along time-like paths, the Wilson lines puncturing the
boundary are the analogs of flat space Faddeev-Kulish dressings. We focus on
the Schwarzschild black hole where our framework provides a
quantum-field-theoretical perspective of the Hawking-Perry-Strominger viewpoint
that black holes carry soft hair, through a study of the Wilson line dressings,
localized on the horizon.
