A Scattering Theory Based on Free Fields

TL;DR

This paper demonstrates a scattering theory in 1+1 dimensions where free particles can produce solitons, suggesting potential extensions to four dimensions, and challenges existing axioms for local observable algebras.

Contribution

It introduces a model showing free particles can generate solitons upon scattering, expanding the understanding of free field interactions beyond quasifree fields.

Findings

Two ingoing free particles can produce outgoing solitons with positive probability

The model's results can be explicitly computed in 1+1 dimensions

The approach may extend to four-dimensional theories

Abstract

So far only quasifree fields have been shown to satisfy the Haag-Araki axioms for local algebras of observables; we show from a model in 1 + 1 dimensions that there can be representations in which two ingoing free particles produce a pair of out-going solitons with positive probability, which can be computed. This happens when the experiment is designed to observe this outcome. It is proposed that the same idea will work in four dimensions.