Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields

TL;DR

This paper develops effective models for quantum particles interacting with quantized electromagnetic fields in the quasi-classical regime, demonstrating well-posedness without ultraviolet cut-offs for point-like particles.

Contribution

It introduces a rigorous framework for effective Schrödinger operators describing quantum particles coupled to large-excitation electromagnetic fields without ultraviolet regularization.

Findings

Effective models are well-posed for point-like particles.

No ultraviolet cut-off is needed in the models.

The approach applies to systems with large field excitations.

Abstract

We study effective models describing systems of quantum particles interacting with quantized (electromagnetic) fields in the quasi-classical regime, i.e., when the field's state shows a large average number of excitations. Once the field's degrees of freedom are traced out on factorized states, the reduced dynamics of the particles' system is described by an effective Schr\"{o}dinger operator keeping track of the field's state. We prove that, under suitable assumptions on the latter, such effective models are well-posed even if the particles are point-like, that is no ultraviolet cut-off is imposed on the interaction with quantum fields.