Scattering matrix and inclusive scattering matrix in algebraic quantum field theory

TL;DR

This paper develops a framework for inclusive scattering matrices within algebraic quantum field theory, enabling analysis of particle and quasiparticle collisions even when traditional unitary scattering matrices are absent.

Contribution

It introduces a novel construction of inclusive scattering matrices expressed via generalized Green functions, extending scattering theory to non-particle interpretations.

Findings

Inclusive scattering matrix expressed in terms of Green functions

Applicable when traditional scattering matrix does not exist

Enables analysis of quasiparticle collisions

Abstract

We study the scattering of particles and quasiparticles in the framework of algebraic quantum field theory. The main novelty is the construction of inclusive scattering matrix related to inclusive cross-sections. The inclusive scattering matrix can be expressed in terms of generalized Green functions by a formula similar to the LSZ formula for the conventional scattering matrix. The consideration of inclusive scattering matrix is necessary in quantum field theory if a unitary scattering matrix does not exist (if the theory does not have particle interpretation). It is always necessary if we want to consider collisions of quasiparticles.