Classical limit of the Pauli-Fierz dynamics

TL;DR

This paper rigorously derives the classical Newton-Maxwell equations from the quantum Pauli-Fierz model in the limit as Planck's constant approaches zero, providing explicit convergence estimates.

Contribution

It offers a new, explicit rate of convergence for the classical limit of the Pauli-Fierz quantum dynamics, extending previous derivations.

Findings

Derived Newton-Maxwell equations as classical limit of quantum dynamics

Provided explicit estimates on the convergence rate

Validated the classical approximation for specific initial data

Abstract

We study the Schr\"odinger evolution generated by the Pauli-Fierz Hamiltonian, a model for nonrelativistic quantum electrodynamics, in the classical limit $\hbar \rightarrow 0$. In this regime, we rigorously derive the Newton-Maxwell equations of classical electrodynamics as effective dynamics approximating the time evolution. Our result complements prior work by an alternative derivation that provides explicit estimates on the rate of convergence, justifying the validity of the approximation for a special class of initial data.