Functional integral approach to semi-relativistic Pauli-Fierz models

TL;DR

This paper employs functional integration techniques to analyze spectral properties of semi-relativistic Pauli-Fierz Hamiltonians in quantum electrodynamics, establishing self-adjointness, decay properties, and ground state measures.

Contribution

It introduces two self-adjoint extensions of the semi-relativistic Pauli-Fierz Hamiltonian and proves key spectral and ground state properties.

Findings

Proved essential self-adjointness of the Hamiltonian

Established spatial decay of bound states

Demonstrated Gaussian domination of the ground state

Abstract

By means of functional integrations spectral properties of semi-relativistic Pauli-Fierz Hamiltonians in quantum electrodynamics is considered. Two self-adjoint extensions of a semi-relativistic Pauli-Fierz Hamiltonian are defined. An essential self-adjointness, a spatial decay of bound states, a Gaussian domination of the ground state and the existence of a measure associated with the ground state are shown.