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Generalized collective coordinate quantization of solitons with topological terms

Taichi Tsukamoto*

  • *Contact author: taichi.t@gauge.scphys.kyoto-u.ac.jp
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Phys. Rev. D 113, 045014 – Published 18 February, 2026

DOI: https://doi.org/10.1103/rykk-vzby

Abstract

For the solitons of the theory including topological terms, the standard collective coordinate quantization does not construct the proper low energy effective theory. In the presence of topological terms, zero modes are classified into three groups: dynamical zero modes with constant velocity, cyclotron zero modes in a circular orbit, and static constraint zero modes. According to the mode expansion, the topological term contributes to the moduli metric of the dynamical zero modes. In addition, constraint zero modes do not have the kinetic term and produce constraints that strongly restrict the spectrum instead. In this paper, we propose a generalized collective coordinate quantization method and apply it to the SU(3) Skyrmion with the Wess-Zumino-Witten term. We find five constraints. These reproduce the results of Cherman et al. [The collective quantization of three-flavored skyrmions revisited, Phys. Rev. D 72, 094015 (2005)], eliminating all the SU(3) multiplets except the nucleon octet and Δ baryon decuplet from the collective coordinate part of the spectrum.

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References (28)

  1. See, e.g., [2] for a review.

  2. N. S. Manton and P. Sutcliffe, Topological Solitons, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2004).
  3. U. G. Meissner, Low-energy hadron physics from effective chiral Lagrangians with vector mesons, Phys. Rep. 161, 213 (1988).
  4. G. S. Adkins, C. R. Nappi, and E. Witten, Static properties of nucleons in the skyrme model, Nucl. Phys. B228, 552 (1983).
  5. G. Panico and A. Wulzer, Nucleon form factors from 5D skyrmions, Nucl. Phys. A825, 91 (2009).
  6. E. Guadagnini, Baryons as solitons and mass formulae, Nucl. Phys. B236, 35 (1984).
  7. M. Chemtob, Skyrme model of baryon octet and decuplet, Nucl. Phys. B256, 600 (1985).
  8. D. Diakonov, V. Petrov, and M. V. Polyakov, Exotic anti-decuplet of baryons: Prediction from chiral solitons, Z. Phys. A 359, 305 (1997).

  9. For the experiments and their results, see [10] or [11], for example.

  10. M. Praszalowicz, 20 years of Θ+, Proc. Sci. CORFU2023 (2024) 063 [arXiv:2405.09926].
  11. M. Amaryan, 20 years of light pentaquark searches, Acta Phys. Pol. B 56, 3-A9 (2025).
  12. C. G. Callan, Jr. and I. R. Klebanov, Bound state approach to strangeness in the skyrme model, Nucl. Phys. B262, 365 (1985).
  13. C. G. Callan, Jr., K. Hornbostel, and I. R. Klebanov, Baryon masses in the bound state approach to strangeness in the skyrme model, Phys. Lett. B 202, 269 (1988).
  14. N. Itzhaki, I. R. Klebanov, P. Ouyang, and L. Rastelli, Is Θ+(1540) a kaon skyrmion resonance?, Nucl. Phys. B684, 264 (2004).
  15. A. Cherman, T. D. Cohen, T. R. Dulaney, and E. M. Lynch, The collective quantization of three-flavored skyrmions revisited, Phys. Rev. D 72, 094015 (2005).
  16. H. Walliser and H. Weigel, Bound state versus collective coordinate approaches in chiral soliton models and the width of the Θ+ pentaquark, Eur. Phys. J. A 26, 361 (2005).
  17. J.-L. Gervais and B. Sakita, Extended particles in quantum field theories, Phys. Rev. D 11, 2943 (1975).
  18. T. D. Cohen and W. Broniowski, Semiclassical projection of Hedgehog models with quarks, Phys. Rev. D 34, 3472 (1986).
  19. E. Witten, Global aspects of current algebra, Nucl. Phys. B223, 422 (1983).
  20. E. Witten, Current algebra, baryons, and quark confinement, Nucl. Phys. B223, 433 (1983).
  21. P. O. Mazur, M. A. Nowak, and M. Praszalowicz, SU(3) Extension of the skyrme model, Phys. Lett. 147B, 137 (1984).
  22. T. H. R. Skyrme, A unified field theory of mesons and baryons, Nucl. Phys. 31, 556 (1962).
  23. N. S. Manton, Skyrmions and their pion multipole moments, Acta Phys. Pol. B 25, 1757 (1994).
  24. S. N. Gupta, Theory of longitudinal photons in quantum electrodynamics, Proc. Phys. Soc. London Sect. A 63, 681 (1950).
  25. K. Bleuler, A new method of treatment of the longitudinal and scalar photons, Helv. Phys. Acta 23, 567 (1950).
  26. Z. Hasiewicz, J. Kowalski-Glikman, J. Lukierski, and J. W. van Holten, BRST formulation of the Gupta-Bleuler quantization method, J. Math. Phys. (N.Y.) 32, 2358 (1991).
  27. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  28. T. D. Cohen, Comment on the Walliser-Weigel approach to exotic baryons in chiral soliton models, arXiv:hep-ph/0511174.

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Phys. Rev. D 113, 045014– Published 18 February, 2026
  • Received 20 June 2025
  • Accepted 20 January 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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