Mechanical form factors and densities of non-relativistic fermions

TL;DR

This paper develops Galilei-covariant expressions for mechanical form factors and densities of non-relativistic fermions, clarifying their internal structure and quantum effects, with implications for hadron physics analogies.

Contribution

It introduces Galilei-covariant breakdowns of energy-momentum tensor matrix elements and analyzes associated spatial densities for spin-half states in non-relativistic quantum systems.

Findings

Derived Galilei-covariant form factors for non-relativistic fermions.

Analyzed spatial densities using pilot wave interpretation.

Provided non-relativistic Breit frame densities.

Abstract

The hadron physics community has been actively debating the interpretation of so-called mechanical properties of hadrons. Non-relativistic quantum-mechanical systems like the hydrogen atom have been appealed to in these debates as analogies. Since such appeals are likely to continue, it is important to have Galilei-covariant expressions for matrix elements of the energy-momentum tensor. In this work, I obtain Galilei-covariant breakdowns of such matrix elements into mechanical form factors, with a special focus on spin-half states. I additionally study the spatial densities associated with these form factors, using the pilot wave interpretation to guide their breakdown into contributions from internal structure and from quantum-mechanical effects such as wave packet dispersion. For completeness, I also obtain non-relativistic Breit frame densities.