Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

External sources in pseudoquantum electrodynamics

L. H. C. Borges*

A. A. Nogueira†

F. A. Barone‡

  • *Contact author: luizhenrique.borges@ufla.br
  • †Contact author: andsogueira@hotmail.com
  • ‡Contact author: fbarone@unifei.edu.br

Phys. Rev. D 114, 085007 – Published 8 October, 2026

DOI: https://doi.org/10.1103/ff1q-5cgy

Abstract

In this paper, we investigate the interaction between stationary pointlike external sources within the framework of pseudoquantum electrodynamics (PQED). Besides ordinary electric charges, we consider configurations involving Dirac points and generalized topological sources. For the configurations analyzed, we compute the corresponding interaction energies, forces, torques, and electromagnetic field configurations. Furthermore, we compare the results obtained in PQED with those arising in ordinary planar Maxwell electrodynamics, showing that the nonlocal character of PQED gives rise to physical effects with no counterpart in the conventional local planar theory. In particular, our results show that topological sources induce intrinsically anisotropic and noncentral interactions, leading to the emergence of nontrivial torques between the interacting objects. The directional character of these interactions suggests possible applications in the effective description of topological defects and anisotropic phenomena in planar condensed matter systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (46)

  1. E. C. Marino, Nucl. Phys. B408, 551 (1993).
  2. E. C. Marino, Phys. Lett. B 263, 63 (1991).
  3. V. S. Alves, W. S. Elias, L. O. Nascimento, V. Juričić, and F. Peña, Phys. Rev. D 87, 125002 (2013).
  4. S. Teber and A. V. Kotikov, Europhys. Lett. 107, 57001 (2014).
  5. E. Barnes, E. H. Hwang, R. E. Throckmorton, and S. Das Sarma, Phys. Rev. B 89, 235431 (2014).
  6. L. O. Nascimento, V. S. Alves, F. Peña, C. M. Smith, and E. C. Marino, Phys. Rev. D 92, 025018 (2015).
  7. E. C. Marino, L. O. Nascimento, V. S. Alves, and C. M. Smith, Phys. Rev. X 5, 011040 (2015).
  8. N. Menezes, V. S. Alves, and C. M. Smith, Eur. Phys. J. B 89, 271 (2016).
  9. A. V. Kotikov and S. Teber, Phys. Rev. D 94, 114010 (2016).
  10. V. S. Alves, R. O. C. Junior, E. C. Marino, and L. O. Nascimento, Phys. Rev. D 96, 034005 (2017).
  11. N. Menezes, V. S. Alves, E. C. Marino, L. Nascimento, L. O. Nascimento, and C. Morais Smith, Phys. Rev. B 95, 245138 (2017).
  12. G. C. Magalhães, V. S. Alves, E. C. Marino, and L. O. Nascimento, Phys. Rev. D 101, 116005 (2020).
  13. J. A. C. Olivares, L. Albino, A. J. Mizher, and A. Raya, Phys. Rev. D 102, 096023 (2020).
  14. R. F. Ozela, V. S. Alves, G. C. Magalhães, and L. O. Nascimento, Phys. Rev. D 105, 056004 (2022).
  15. L. Albino, A. Bashir, A. J. Mizher, and A. Raya, Phys. Rev. D 106, 096007 (2022).
  16. J. A. Casimiro Olivares, A. J. Mizher, and A. Raya, Rev. Mex. Fís. 68, 040101 (2022).
  17. V. N. Kotov, B. Uchoa, V. M. Pereira, F. Guinea, and A. H. Castro Neto, Rev. Mod. Phys. 84, 1067 (2012).
  18. V. S. Alves, E. Marino, L. O. Nascimento, J. Medeiros Neto, R. F. Ozela, and R. O. Ramos, Phys. Lett. B 797, 134860 (2019).
  19. R. F. Ozela, V. S. Alves, E. C. Marino, L. O. Nascimento, J. F. Medeiros Neto, R. O. Ramos, and C. Morais Smith, arXiv:1907.11339.
  20. R. F. Ozela, V. S. Alves, L. O. Nascimento, E. C. Marino, C. Morais Smith, R. O. Ramos, and J. F. Medeiros Neto, Phys. Rev. D 108, 056017 (2023).
  21. V. S. Alves, T. Macrì, G. C. Magalhães, E. C. Marino, and L. O. Nascimento, Phys. Rev. D 97, 096003 (2018).
  22. Y.-Hui. Xing, L. Zhuang, E. C. Marino, and W.-Ming. Liu, Phys. Rev. B 108, L220504 (2023).
  23. M. J. Neves, Phys. Rev. D 111, 016009 (2025).
  24. M. J. Neves, Phys. Lett. B 869, 139818 (2025).
  25. M. J. Neves, Eur. Phys. J. C 86, 87 (2026).
  26. M. I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, Cambridge, England, 2012).
  27. L. H. C. Borges, F. E. Barone, C. C. H. Ribeiro, H. L. Oliveira, R. L. Fernandez, and F. A. Barone, Eur. Phys. J. C 80, 238 (2020).
  28. L. H. C. Borges, F. A. Barone, and H. L. Oliveira, Phys. Rev. D 105, 025008 (2022).
  29. L. H. C. Borges, A. F. Ferrari, P. H. O. da Silva, and F. A. Barone, Ann. Phys. (Amsterdam) 469, 169749 (2024).
  30. F. A. Barone, H. L. Oliveira, and J. P. Ferreira, Phys. Rev. D 112, 065013 (2025).
  31. Eduardo C. Marino, Leandro O. Nascimento, Van Sérgio Alves, and Danilo T. Alves, Entropy 26, 925 (2024).
  32. R. L. P. G. do Amaral and E. C. Marino, J. Phys. A 25, 5183 (1992).
  33. E. C. Marino, L. O. Nascimento, V. S. Alves, and C. Morais Smith, Phys. Rev. D 90, 105003 (2014).
  34. D. Dudal, A. J. Mizher, and P. Pais, Phys. Rev. D 99, 045017 (2019).
  35. M. Heydeman, C. B. Jepsen, Z. Ji, and A. Yarom, J. High Energy Phys. 08 (2020) 007.
  36. L. H. C. Borges and F. A. Barone, Phys. Lett. B 824, 136759 (2022).
  37. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, Cambridge, 2000).
  38. F. A. Barone and G. Flores-Hidalgo, Phys. Rev. D 78, 125003 (2008).
  39. L. H. C. Borges and F. A. Barone (to be published).
  40. F. A. Barone and G. Flores-Hidalgo, Braz. J. Phys. 40, 188 (2010).
  41. M. A. H. Vozmediano, M. I. Katsnelson, and F. Guinea, Phys. Rep. 496, 109 (2010).
  42. B. Amorim et al., Phys. Rep. 617, 1 (2016).
  43. A. Cortijo and M. A. H. Vozmediano, Nucl. Phys. B763, 293 (2007).
  44. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
  45. F. Guinea, M. I. Katsnelson, and A. K. Geim, Nat. Phys. 6, 30 (2010).
  46. H. L. Oliveira, L. H. C. Borges, F. E. Barone, and F. A. Barone, Eur. Phys. J. C 81, 558 (2021).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation