2024/07/30 by Marco Falconi, Falconi, Marco, Lorenzo Fratini +1 · 1 citation
Computer Science · Physics and Astronomy · #43A95 #46N50 #81S05 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Operator Algebras (math.OA) #Primary: 81T05. Secondary: 81Q20 #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2407.20603
openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the semiclassical limit \hslash→ 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.