IR finite S-matrix by gauge invariant dressed states

Understand

Dressed states were proposed to define the infrared (IR) finite $S$-matrix in QED or gravity.

• We show that the original Kulish-Faddeev dressed states are not enough to cure the IR divergences.
• To illustrate this problem, we consider QED with background currents (Wilson lines).
• This theory is exactly solvable but shares the same IR problems as the full QED.