A direct derivation of an effective Hamiltonian in non-relativistic quantum electrodynamics

TL;DR

This paper derives an effective Hamiltonian in non-relativistic quantum electrodynamics directly, broadening applicability to various potentials without using the scaling limit.

Contribution

It provides a new direct derivation of Arai's effective Hamiltonian applicable to a wider class of potentials, including confining ones.

Findings

Derivation applicable to Rollnik class potentials

Extension to confining potentials like harmonic potential

No reliance on the scaling limit in derivation

Abstract

We present a direct derivation of Arai's effective Hamiltonian in non-relativistic quantum electrodynamics without relying on the scaling limit. Our result applies to a broader class of potentials, including the Rollnik class and confining potentials such as the harmonic potential.