Abstract semiclassical analysis of the van Hove model

TL;DR

This paper investigates the semiclassical limit of the solvable van Hove quantum field model, revealing how classical behavior emerges from quantum dynamics and states, especially considering infrared singularities.

Contribution

It applies recent representation-independent semiclassical techniques to analyze the van Hove model, establishing the Bohr correspondence principle in this context.

Findings

Established the Bohr correspondence principle for the van Hove model.

Analyzed the emergence of classical dynamics in the semiclassical limit.

Studied the behavior of non-Fock ground and equilibrium states with infrared singularities.

Abstract

In this paper we study the semiclassical limit $\hslash\to 0$ of a completely solvable model in quantum field theory: the van Hove model, describing a scalar field created and annihilated by an immovable source. Despite its simplicity, the van Hove model possesses many characterizing features of quantum fields, especially in the infrared region. In particular, the existence of non-Fock ground and equilibrium states in the presence of infrared singular sources makes a representation-independent algebraic approach of utmost importance. We make use of recent representation-independent techniques of infinite dimensional semiclassical analysis to establish the Bohr correspondence principle for the dynamics, equilibrium states, and long-time asymptotics in the van Hove model.