Renormalization for a model of photon scattering off a charged harmonic oscillator

TL;DR

This paper examines a solvable model of photon scattering by a charged harmonic oscillator, highlighting the necessity of a finite UV cutoff for physical consistency and renormalizability.

Contribution

It clarifies the role of the UV cutoff in the model, showing that renormalizability is only apparent and the cutoff must remain finite for accurate physical predictions.

Findings

The model is quadratic and solvable in the electric dipole approximation.

Renormalizability depends on keeping the UV cutoff finite.

The cutoff parameter influences the high-frequency behavior of the photon cross section.

Abstract

In the electric dipole approximation the model of a charged harmonic oscillator interacting with the radiation field becomes quadratic and soluble, but it needs a UV cutoff for the photon frequency. The model's renormalizability is only apparent; physics requires that the cutoff be kept finite. The cutoff plays the role of a parameter that characterizes the high frequency behavior of the photon cross section.