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

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 Poincaré generators in order to derive constraints on these form factors as $q\to 0$. 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 Poincaré 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 Poincaré transformations.

arXiv comment11 pages; v2: additional comments added, matches published version

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