IR finite S-matrix by gauge invariant dressed states

TL;DR

This paper demonstrates that traditional dressed states are insufficient for IR finiteness in QED and proposes new dressed states aligned with asymptotic symmetries to achieve an IR finite S-matrix.

Contribution

The authors introduce new gauge-invariant dressed states that resolve IR divergences and are consistent with asymptotic symmetries in QED.

Findings

Original Kulish-Faddeev states are inadequate for IR finiteness.

Naive asymptotic states lead to IR divergences and symmetry inconsistencies.

New dressed states yield an IR finite S-matrix.

Abstract

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. We show that naive asymptotic states lead to IR divergences in the $S$-matrix and are also inconsistent with the asymptotic symmetry, even if we add the original Kulish-Faddeev dressing operators. We then propose new dressed states which are consistent with the asymptotic symmetry. We show that the $S$-matrix for the dressed states is IR finite. We finally conclude that appropriate dressed asymptotic states define the IR finite $S$-matrix in the full QED.