Rigorous Dynamics and Radiation Theory for a Pauli-Fierz Model in the Ultraviolet Limit

TL;DR

This paper rigorously analyzes the dynamics and radiation processes of a charged oscillator interacting with an electromagnetic field in the ultraviolet limit, providing explicit quantum evolution and insights into decay and emission phenomena.

Contribution

It introduces a well-defined classical and quantum framework for the point limit of the Pauli-Fierz model, including the derivation of exact survival amplitudes and Lamb shift corrections.

Findings

Exact time behavior of survival amplitudes determined by system resonances.

Identification of tail terms influencing long-time decay behavior.

Explicit quantization scheme for the point limit of the Pauli-Fierz model.

Abstract

The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behaviour of the survival and transition amplitudes for the process of decay of the excited states of the charged particle, and the emission of photons in the decay process. In particular, for the survival amplitude the exact time behaviour is found. This is completely determined by the resonances of the systems plus a tail term prevailing in the asymptotic, long time regime. Moreover, the survival amplitude exhibites in a fairly clear way the Lamb shift correction to the unperturbed frequencies of the oscillator.