# 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 → 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.

- Authors:

- SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1393987

- Alternate Identifier(s):
- OSTI ID: 1443873

- Report Number(s):
- SLAC-PUB-17111

Journal ID: ISSN 0370-2693; PII: S0370269317307621

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physics Letters. Section B

- Additional Journal Information:
- Journal Volume: 774; Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Energy–momentum tensor; Form factor; Anomalous gravitomagnetic moment

### Citation Formats

```
Lowdon, Peter, Chiu, Kelly Yu-Ju, and Brodsky, Stanley J.
```*Rigorous constraints on the matrix elements of the energy–momentum tensor*. United States: N. p., 2017.
Web. doi:10.1016/j.physletb.2017.09.050.

```
Lowdon, Peter, Chiu, Kelly Yu-Ju, & Brodsky, Stanley J.
```*Rigorous constraints on the matrix elements of the energy–momentum tensor*. United States. doi:10.1016/j.physletb.2017.09.050.

```
Lowdon, Peter, Chiu, Kelly Yu-Ju, and Brodsky, Stanley J. Thu .
"Rigorous constraints on the matrix elements of the energy–momentum tensor". United States.
doi:10.1016/j.physletb.2017.09.050.
```

```
@article{osti_1393987,
```

title = {Rigorous constraints on the matrix elements of the energy–momentum tensor},

author = {Lowdon, Peter and Chiu, Kelly Yu-Ju and Brodsky, Stanley J.},

abstractNote = {The structure of the matrix elements of the energy–momentum tensor play an important role in determining the properties of the form factors A(q2), B(q2) and C(q2) 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 → 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.},

doi = {10.1016/j.physletb.2017.09.050},

journal = {Physics Letters. Section B},

number = C,

volume = 774,

place = {United States},

year = {Thu Sep 21 00:00:00 EDT 2017},

month = {Thu Sep 21 00:00:00 EDT 2017}

}

*Citation information provided by*

Web of Science

Web of Science