Relativistic properties of a molecule: energy, linear momentum, angular momentum and boost momentum to order $1/c^2$

TL;DR

This paper provides a detailed relativistic analysis of a molecule's energy and momentum, including subtle effects like Hall shifts and anomalous velocities, up to order 1/c^2, incorporating electron, nucleus, and electromagnetic contributions.

Contribution

It offers a comprehensive and explicit description of molecular relativistic properties to order 1/c^2, highlighting subtle effects not seen at lower orders.

Findings

Identification of relativistic Hall shifts

Discovery of anomalous velocities in molecules

Analysis of hidden momenta in molecular systems

Abstract

We give an explicit and general description of the energy, linear momentum, angular momentum and boost momentum of a molecule to order $1/c^2$, where it necessary to take account of kinetic contributions made by the electrons and nuclei as well as electromagnetic contributions made by the intramolecular field. A wealth of interesting subtleties are encountered that are not seen at order $1/c^0$, including relativistic Hall shifts, anomalous velocities and hidden momenta. Some of these have well known analogues in solid state physics.