Rigorous constraints on the matrix elements of the energy-momentum tensor

TL;DR

This paper derives fundamental, frame-independent constraints on the form factors of the energy-momentum tensor, clarifying their independence and the physical principles underlying these constraints.

Contribution

It introduces a rigorous distributional-matching approach to derive constraints on energy-momentum tensor form factors, emphasizing their independence and physical origin.

Findings

Demonstrates that $B(0)$ and $A(0)$ constraints are independent.

Shows constraints stem from on-shell state properties and Poincaré transformations.

Clarifies misconceptions about the relation between form factor constraints.

Abstract

The structure of the matrix elements of the energy-momentum tensor play an important role in determining the properties of the form factors $A(q^{2})$, $B(q^{2})$ and $C(q^{2})$ which appear in the Lorentz covariant decomposition of the matrix elements. In this paper we apply a rigorous frame-independent distributional-matching approach to the matrix elements of the Poincar\'{e} generators in order to derive constraints on these form factors as $q \rightarrow 0$. In contrast to the literature, we explicitly demonstrate that the vanishing of the anomalous gravitomagnetic moment $B(0)$ and the condition $A(0)=1$ are independent of one another, and that these constraints are not related to the specific properties or conservation of the individual Poincar\'{e} generators themselves, but are in fact a consequence of the physical on-shell requirement of the states in the matrix elements and the manner in which these states transform under Poincar\'{e} transformations.