Compton scattering in the Buchholz-Roberts framework of relativistic QED

TL;DR

This paper develops a new approach to Compton scattering in relativistic QED within the Buchholz-Roberts framework, demonstrating that massive particle states are vacua for massless fields and constructing the outgoing wave operator.

Contribution

It introduces a novel technique based on the Mean Ergodic Theorem to analyze scattering and simplifies the infrared problem in the Buchholz-Roberts setting.

Findings

Massive particle states are vacua for massless asymptotic fields.

Constructed the outgoing isometric wave operator for Compton scattering.

Simplified the scattering theory of massless bosons in the vacuum sector.

Abstract

We consider a Haag-Kastler net in a positive energy representation, admitting massive Wigner particles and asymptotic fields of massless bosons. We show that states of the massive particles are always vacua of the massless asymptotic fields. Our argument is based on the Mean Ergodic Theorem in a certain extended Hilbert space. As an application of this result we construct the outgoing isometric wave operator for Compton scattering in QED in a class of representations recently proposed by Buchholz and Roberts. In the course of this analysis we use our new technique to further simplify scattering theory of massless bosons in the vacuum sector. A general discussion of the status of the infrared problem in the setting of Buchholz and Roberts is given.