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The energy-momentum tensor in a classical model of the electron

Grace Gardella, Mira Varma, Peter Schweitzer

Abstract

We show that the leading non-analytic terms in the small-t expansion of the energy momentum tensor (EMT) form factors of an electrically charged particle in QED can be correctly derived in a classical model of the electron by Bialynicki-Birula. Based on the lucidity of the employed exactly solvable model, we comment also on the recently proposed concept of a regularized proton D-term.

The energy-momentum tensor in a classical model of the electron

Abstract

We show that the leading non-analytic terms in the small-t expansion of the energy momentum tensor (EMT) form factors of an electrically charged particle in QED can be correctly derived in a classical model of the electron by Bialynicki-Birula. Based on the lucidity of the employed exactly solvable model, we comment also on the recently proposed concept of a regularized proton D-term.
Paper Structure (9 sections, 30 equations, 1 figure)

This paper contains 9 sections, 30 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Classical Model of the Electron
  3. The spatial EMT distributions in the electron model
  4. Energy density $T_{00}(r)$
  5. The $T_{0k}$ components
  6. The stress tensor $T_{ij}$
  7. The EMT form factors $A(t)$ and $D(t)$
  8. Comments on proton $D$-term regularization of Refs. Varma:2020crxMejia:2025oip
  9. Conclusions

Figures (1)

  • Figure 1: Electron model EMT distributions as functions of $r$ in units of electron radius $R$. (a) Energy distribution $T_{00}(r)$ in units of $M/R^3$. (b) The stress tensor distributions $s(r)$ and $p(r)$ in units of $|p_0|$. (c) The distribution of $r^2p(r)$ in units of $R^2|p_0|$ illustrating how the von Laue condition in Eq. (\ref{['Eq:von-Laue']}b) is satisfied. The sign patterns of the stress tensor distributions $s(r)$ and $p(r)$ are opposite to what has been found in hadronic models based on short-range interactions.