Massless asymptotic fields and Haag-Ruelle theory

TL;DR

This paper extends Haag-Ruelle theory to massless quantum fields, providing a more general framework for null asymptotes without relying on strict locality or vacuum assumptions.

Contribution

It introduces a new approach to construct massless asymptotic fields using weak decay conditions and spectral properties, broadening the applicability of Haag-Ruelle theory.

Findings

Established existence of null asymptotes for weakly decaying fields

Linked asymptotic fields to spectral properties near the lightcone

Unified massive and massless field asymptotic analysis

Abstract

We revisit the problem of the existence of asymptotic massless boson fields in quantum field theory. The well-known construction of such fields by Buchholz [2], [4] is based on locality and the existence of vacuum vector, at least in regions spacelike to spacelike cones. Our analysis does not depend on these assumptions and supplies a more general framework for fields only very weakly decaying in spacelike directions. In this setting the existence of appropriate null asymptotes of fields is linked with their spectral properties in the neighborhood of the lightcone. The main technical tool is one of the results of a recent analysis by one of us [11], which allows application of the null asymptotic limit separately to creation/annihilation parts of a wide class of non-local fields. In vacuum representation the scheme allows application of the methods of the Haag-Ruelle theory closely analogous to those of the massive case. In local case this Haag-Ruelle procedure may be combined with the Buchholz method, which leads to significant simplification.