Strengthened Reeh-Schlieder Property and Scattering in Quantum Field Theories without Mass Gaps

TL;DR

This paper extends Haag-Ruelle scattering theory to massless particles in local relativistic quantum field theories by strengthening the Reeh-Schlieder property, enabling the construction of scattering states without mass gap assumptions.

Contribution

It introduces a strengthened Reeh-Schlieder property that allows scattering theory development without the need for a mass gap in quantum field theories.

Findings

Scattering states can be constructed without mass gaps.

A strengthened Reeh-Schlieder property is sufficient for scattering theory.

The approach applies to theories with massless particles.

Abstract

We develop Haag-Ruelle scattering theory for Wigner particles in local relativistic Quantum Field Theory without assuming mass gaps or any other restrictions on the spectrum of the mass operator near the particle masses. Our approach is based on the Reeh-Schlieder property of the vacuum state. It is shown that a strengthened variant of this property, concerning the relative approximation error for single-particle states, implies the existence of scattering states.