# Pauli-Fierz type operators with singular electromagnetic potentials on general domains

## TL;DR

This paper studies Dirichlet and Neumann realizations of Pauli-Fierz operators on general domains, establishing domain characterizations and extending previous results to unbounded and singular potentials with local irregularities.

## Contribution

It provides new conditions for domain determination of Pauli-Fierz operators on arbitrary domains, including unbounded and singular potentials, extending prior Euclidean space results.

## Key findings

- Domains are characterized by Dirichlet-Schrödinger operators and radiation field energy.
- Results include unbounded electrostatic potentials with local singularities.
- Extension to Neumann realizations on Lipschitz domains.

## Abstract

We consider Dirichlet realizations of Pauli-Fierz type operators generating the dynamics of non-relativistic matter particles which are confined to an arbitrary open subset of the Euclidean position space and coupled to quantized radiation fields. We find sufficient conditions under which their domains and a natural class of operator cores are determined by the domains and operator cores of the corresponding Dirichlet-Schr\"{o}dinger operators and the radiation field energy. Our results also extend previous ones dealing with the entire Euclidean space, since the involved electrostatic potentials might be unbounded at infinity with local singularities that can only be controlled in a quadratic form sense, and since locally square-integrable classical vector potentials are covered as well. We further discuss Neumann realizations of Pauli-Fierz type operators on Lipschitz domains.