Definition of gravitational local spatial densities for spin-0 and spin-1/2 systems

TL;DR

This paper develops a detailed framework for defining gravitational local spatial densities in spin-0 and spin-1/2 systems using localized wave packets, applicable in various momentum frames.

Contribution

It provides explicit expressions for gravitational spatial densities in different reference frames, advancing the understanding of gravitational form factors in quantum systems.

Findings

Derived expressions for spatial densities in zero-momentum frame

Extended definitions to non-zero momentum frames

Clarified the relation between form factors and spatial distributions

Abstract

We work out details of defining the spatial densities corresponding to the gravitational form factors of spin-0 and spin-1/2 systems using spherically symmetric sharply localized wave packets. The expressions for the spatial densities are provided in the frames with both zero and non-zero expectation values of the momentum operator.