Perspective: Quantum Hamiltonians for Optical Interactions

TL;DR

This paper clarifies the theoretical foundations of the multipolar Hamiltonian in quantum electrodynamics, affirming its physical validity and addressing recent concerns about gauge invariance and observable equivalence.

Contribution

It provides an in-depth analysis that defends the Power-Zienau-Woolley Hamiltonian's validity and clarifies misconceptions about gauge invariance in quantum electrodynamics.

Findings

The PZW Hamiltonian is based on solid physical principles.

Claims of non-physicality are refuted.

Theoretical foundations of gauge transformations are clarified.

Abstract

The multipolar Hamiltonian of quantum electrodynamics (QED) is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.