The role of infrared divergence for decoherence

TL;DR

This paper investigates how infrared divergence in a Boson field environment leads to decoherence and superselection sectors, providing exact models and conditions for their emergence.

Contribution

It introduces exactly solvable Hamiltonian models showing that infrared divergence causes superselection sectors by eliminating the Boson ground state.

Findings

Superselection sectors form when low frequencies dominate.

Infrared divergence causes the Boson ground state to vanish.

Transition matrix elements between sectors can be uniformly estimated.

Abstract

Continuous and discrete superselection rules induced by the interaction with the environment are investigated for a class of exactly soluble Hamiltonian models. The environment is given by a Boson field. Stable superselection sectors emerge if and only if the low frequences dominate and the ground state of the Boson field disappears due to infrared divergence. The models allow uniform estimates of all transition matrix elements between different superselection sectors.