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Energy-momentum tensor in a classical model of the electron
Phys. Rev. D 113, 116008 – Published 4 June, 2026
DOI: https://doi.org/10.1103/zp92-8sd5
Abstract
We show that the leading nonanalytic terms in the small- expansion of the energy-momentum tensor form factors of an electrically charged particle in QED can be correctly derived in a classical model of the electron by Białynicki-Birula. Based on the lucidity of the employed exactly solvable model, we comment also on the recently proposed concept of a regularized proton -term.
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References (59)
- X. D. Ji, Phys. Rev. D 52, 271 (1995).
- X. D. Ji, Phys. Rev. Lett. 78, 610 (1997).
- M. V. Polyakov and C. Weiss, Phys. Rev. D 60, 114017 (1999).
- X. D. Ji, J. Phys. G 24, 1181 (1998).
- A. V. Radyushkin, arXiv:hep-ph/0101225.
- K. Goeke, M. V. Polyakov, and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 47, 401 (2001).
- M. Diehl, Phys. Rep. 388, 41 (2003).
- A. V. Belitsky and A. V. Radyushkin, Phys. Rep. 418, 1 (2005).
- S. Boffi and B. Pasquini, Riv. Nuovo Cimento 30, 387 (2007).
- M. V. Polyakov, Phys. Lett. B 555, 57 (2003).
- M. V. Polyakov and P. Schweitzer, Int. J. Mod. Phys. A 33, 1830025 (2018).
- V. D. Burkert, L. Elouadrhiri, F. X. Girod, C. Lorcé, P. Schweitzer, and P. E. Shanahan, Rev. Mod. Phys. 95, 041002 (2023).
- C. Lorcé, H. Moutarde, and A. P. Trawiński, Eur. Phys. J. C 79, 89 (2019).
- A. Freese and G. A. Miller, Phys. Rev. D 103, 094023 (2021).
- C. Lorcé and P. Schweitzer, Acta Phys. Pol. B 56, 3-A17 (2025).
- G. A. Miller, Phys. Rev. C 112, 045204 (2025).
- X. Ji and C. Yang, Nucl. Phys. B1024, 117342 (2026).
- R. Hofstadter, Rev. Mod. Phys. 28, 214 (1956).
- F. A. Berends and R. Gastmans, Ann. Phys. (N.Y.) 98, 225 (1976).
- K. A. Milton, Phys. Rev. D 15, 538 (1977).
- B. Kubis and U. G. Meissner, Nucl. Phys. A671, 332 (2000); A692, 647 (2001).
- J. F. Donoghue, B. R. Holstein, B. Garbrecht, and T. Konstandin, Phys. Lett. B 529, 132 (2002); 612, 311(E) (2005).
- M. Varma and P. Schweitzer, Phys. Rev. D 102, 014047 (2020).
- A. Mejia and P. Schweitzer, Phys. Rev. D 113, 054016 (2026).
- A. Metz, B. Pasquini, and S. Rodini, Phys. Lett. B 820, 136501 (2021).
- A. Freese, A. Metz, B. Pasquini, and S. Rodini, Phys. Lett. B 839, 137768 (2023).
- J. Y. Panteleeva, Phys. Rev. D 107, 055015 (2023).
- X. Ji, J. Yang, and Y. Liu, Phys. Rev. D 110, 114045 (2024).
- A. Czarnecki, Y. Liu, and S. N. Reza, Acta Phys. Pol. B Proc. Suppl. 16, 7-A19 (2023).
- A. Freese, Phys. Rev. D 111, 034047 (2025).
- I. Białynicki-Birula, Phys. Rev. D 28, 2114 (1983).
- J. J. Thomson, Electrician 39, 104 (1897); Philos. Mag. Ser. 5 44, 293 (1897).
- P. A. Dirac, Proc. R. Soc. A 268, 57 (1962).
- J. S. Schwinger, Found. Phys. 13, 373 (1983).
- P. Pearle, Classical electron models in electromagnetism, in Paths to Research, edited by D. Teplitz (Plenum, New York, 1982), Chap. 7.
- I. Bialynicki-Birula, Phys. Lett. A 182, 346 (1993).
- F. Rohrlich, Am. J. Phys. 65, 1051 (1997).
- T. H. Boyer, Phys. Rev. D 25, 3246 (1982).
- F. Rohrlich, Phys. Rev. D 25, 3251 (1982).
- See, the Appendix on Units and Dimensions in J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1998).
- H. Poincaré, Rend. Circ. Mat. Palermo 21, 129 (1906).
- S. J. Brodsky and S. D. Drell, Phys. Rev. D 22, 2236 (1980).
- H. Dehmelt, Rev. Mod. Phys. 62, 525 (1990).
- G. Kopp, D. Schaile, M. Spira, and P. M. Zerwas, Z. Phys. C 65, 545 (1995).
- M. Acciarri et al. (L3 Collaboration), Phys. Lett. B 489, 81 (2000).
- M. E. Peskin, arXiv:2003.05435.
- R. Rajamaran, Solitons and Instantons Amsterdam (North-Holland, Amsterdam, 1982).
- M. Laue, Ann. Phys. (Berlin) 340, 524 (1911).
- A. Freese (private communication).
- I. Y. Kobzarev and L. B. Okun, Zh. Eksp. Teor. Fiz. 43, 1904 (1962) [Sov. Phys. JETP 16, 1343 (1963)]; H. Pagels, Phys. Rev. 144, 1250 (1966).
- E. Epelbaum, J. Gegelia, N. Lange, U. G. Meißner, and M. V. Polyakov, Phys. Rev. Lett. 129, 012001 (2022).
- J. Y. Panteleeva, E. Epelbaum, J. Gegelia, and U. G. Meißner, Phys. Rev. D 106, 056019 (2022).
- J. Y. Panteleeva, E. Epelbaum, J. Gegelia, and U. G. Meißner, Eur. Phys. J. C 83, 617 (2023).
- K. Goeke, J. Grabis, J. Ossmann, M. V. Polyakov, P. Schweitzer, A. Silva, and D. Urbano, Phys. Rev. D 75, 094021 (2007).
- K. Goeke, J. Grabis, J. Ossmann, P. Schweitzer, A. Silva, and D. Urbano, Phys. Rev. C 75, 055207 (2007).
- C. Cebulla, K. Goeke, J. Ossmann, and P. Schweitzer, Nucl. Phys. A794, 87 (2007).
- J. Hudson and P. Schweitzer, Phys. Rev. D 96, 114013 (2017).
- J. Hudson and P. Schweitzer, Phys. Rev. D 97, 056003 (2018).
- P. Beißner, B. D. Sun, E. Epelbaum, and J. Gegelia, Eur. Phys. J. C 85, 1471 (2025); P. Beißner, J. Y. Panteleeva, B. D. Sun, E. Epelbaum, and J. Gegelia, arXiv:2601.22731.