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