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High-precision lattice determination of the interaction potential of an SU(2) solitonic dipole and comparison with perturbative QED

Manfried Faber* and Rudolf Golubich†

  • *Contact author: faber@kph.tuwien.ac.at
  • †Contact author: rudolf.golubich@gmail.com
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Phys. Rev. D 114, 014510 – Published 16 July, 2026

DOI: https://doi.org/10.1103/8zn4-rwth

Abstract

We determine the interaction potential of a solitonic dipole in the singlet state, modeled as an SU(2) field, using improved lattice simulations of two stationary solitons at varying separations. The potential is extracted from the energy of two-soliton configurations as a function of distance. At large separations, the interaction reproduces the classical Coulomb potential quantitatively up to an energy shift δE∞≈9  keV of the fitted asymptotic constant relative to 2mec02, assumed to be related to limited numerical precision on the lattice. At shorter distances, deviations from the Coloumb potential of pointlike charges appear, that are in qualitative agreement with the asymptotic formula of perturbative quantum electrodynamics, reflecting the running of the fine-structure constant, with the inverse fine-structure constant (α−1≈137) reproduced.

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References (19)

  1. M. Faber, A model for topological fermions, Few Body Syst. 30, 149 (2001).
  2. M. Faber, A geometric model in 3+1D space-time for electrodynamic phenomena, Universe 8, 73 (2022).
  3. M. Remoissenet, Waves Called Solitons: Concepts and Experiments (Springer, New York, 1996).
  4. Michael E. Peskin and Daniel V. Schroeder, An Introduction To Quantum Field Theory (1st ed.) (Perseus Books Publishing, Reading, Massachusetts, 1995), p. 842.
  5. J. Wabnig, J. Resch, D. Theuerkauf, F. Anmasser, and M. Faber, Numerical evaluation of a soliton pair with long-range interaction, Universe 11, 113 (2025).
  6. P. A. M. Dirac, Quantised singularities in the electromagnetic field, Proc. R. Soc. A 133, 60 (1931).
  7. P. A. M. Dirac, The theory of magnetic poles, Phys. Rev. 74, 817 (1948).
  8. T. T. Wu and C. N. Yang, Some solutions of the classical isotopic gauge field equations, in Properties of Matter Under Unusual Conditions, edited by H. Mark and S. Fernbach (Wiley-Interscience, New York, 1969), pp. 349–354.
  9. T. T. Wu and C. N. Yang, Some remarks about unquantized non-abelian gauge fields, Phys. Rev. D 12, 3843 (1975).
  10. T. T. Wu and C. N. Yang, Static sourceless gauge field, Phys. Rev. D 13, 3233 (1976).
  11. D. Pisello, Nonlinear classical theory of electromagnetism, Int. J. Theor. Phys. 16, 863 (1977).
  12. D. Pisello, Unified field theory with homotopic charge, Int. J. Theor. Phys. 17, 143 (1978).
  13. T. H. R. Skyrme, A Nonlinear theory of strong interactions, Proc. R. Soc. A 247, 260 (1958).
  14. T. H. R. Skyrme, A nonlinear field theory, Proc. R. Soc. A 260, 127 (1961).
  15. A. M. Polyakov, Particle spectrum in quantum field theory, JETP Lett. 20, 194 (1974).
  16. G. ’t Hooft, Magnetic monopoles in unified gauge theories, Nucl. Phys. B79, 276 (1974).
  17. H. Georgi and S. L. Glashow, Unity of all elementary-particle forces, Phys. Rev. Lett. 32, 438 (1974).
  18. N. Manton, The force between ’t Hooft-Polyakov monopoles, Nucl. Phys. B126, 525 (1977).
  19. National Institute of Standards and Technology, CODATA Internationally Recommended 2022 Values of the Fundamental Physical Constants: Inverse Fine-Structure Constant (2024), https://physics.nist.gov/cgi-bin/cuu/Value?alphinv|search_for=alphainv.

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Phys. Rev. D 114, 014510– Published 16 July, 2026
  • Received 15 April 2026
  • Accepted 23 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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