Superselection rules induced by infrared divergence

TL;DR

This paper investigates how infrared divergence in a Boson field leads to superselection rules, showing that such rules emerge when the photon number diverges and are stable under certain perturbations.

Contribution

It provides an exactly solvable model demonstrating the emergence of superselection rules due to infrared divergence in Boson fields, including stability analysis under perturbations.

Findings

Superselection sectors appear only with infrared divergence.

The superselection rules are stable against scattering perturbations.

Time scale of decoherence depends on infrared contributions and initial state properties.

Abstract

Superselection rules induced by the interaction with a mass zero Boson field are investigated for a class of exactly soluble Hamiltonian models. The calculations apply as well to discrete as to continuous superselection rules. The initial state (reference state) of the Boson field is either a normal state or a KMS state. The superselection sectors emerge if and only if the Boson field is infrared divergent, i. e. the bare photon number diverges and the ground state of the Boson field disappears in the continuum. The time scale of the decoherence depends on the strength of the infrared contributions of the interaction and on properties of the initial state of the Boson system. These results are first derived for a Hamiltonian with conservation laws. But in the most general case the Hamiltonian includes an additional scattering potential, and the only conserved quantity is the energy of the total system. The superselection sectors remain stable against the perturbation by the scattering processes.