A special structure of the scattering operator and infrared divergences in quantum electrodynamics

TL;DR

This paper introduces a new approach to infrared divergences in quantum electrodynamics by analyzing the structure of scattering operators and their relation to unperturbed operators, emphasizing the importance of initial and final wave deviations.

Contribution

It presents a novel method using generalized wave operators to address divergence issues by considering deviations of waves from free waves.

Findings

Infrared divergences are linked to unaccounted deviations of initial and final waves.

The structure of scattering operators is constrained by their permutability with unperturbed operators.

The new approach offers insights into divergence problems in quantum electrodynamics.

Abstract

We assume that the unperturbed operators $A_0$ are known. Then, the fact that the scattering operators $S$ and the unperturbed operators $A_0$ are pairwise permutable provides some important information about the structure of the scattering operators. Using this information and the ideas from the theory of generalized wave operators, we present a new approach to the divergence problems in quantum electrodynamics. We show that the so called infrared divergences appeared because the deviations of the initial and final waves from the free waves were not taken into account.