On the self-adjointness and domain of Pauli-Fierz type Hamiltonians

TL;DR

This paper establishes a general theorem on the self-adjointness and domain properties of Pauli-Fierz Hamiltonians, using commutator techniques to handle non-commuting fields, with implications for non-relativistic QED models.

Contribution

It introduces a novel approach to proving self-adjointness for Pauli-Fierz Hamiltonians with non-commuting fields, extending previous results.

Findings

Domain of non-relativistic QED Hamiltonian is independent of coupling constant

Provides a unified framework for self-adjointness proofs in quantum electrodynamics

Handles fields with non-commuting components effectively

Abstract

We prove a general theorem about the self-adjointness and domain of Pauli-Fierz type Hamiltonians. Our proof is based on commutator arguments which allow us to treat fields with non-commuting components. As a corollary it follows that the domain of the Hamiltonian of non-relativistic QED with Coulomb interactions is independent of the coupling constant.