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Vacuum polarization energy of a nonzero radius cosmic string induced spacetime

N. Graham1 and H. Weigel2

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Phys. Rev. D 114, 085004 – Published 6 October, 2026

DOI: https://doi.org/10.1103/27bw-xzhb

Abstract

We calculate the vacuum polarization energy (VPE) of a scalar field in the background of a nonsingular cosmic string in 2+1 spacetime dimensions. Our calculation expresses the VPE as a renormalized sum and integral over scattering data, which can be expressed in terms of Legendre and Bessel functions for the “ballpoint pen” model, analogous to a square well in curvature, and which can be obtained numerically for a generic string profile. We show how relationships between the local density of states, expressed in terms of the Green’s function, and the global density of states, expressed in terms of the Jost function, extend to this curved spacetime background and allow for precise implementation of perturbative renormalization conditions.

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References (24)

  1. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 1982).
  2. P. Candelas, Phys. Rev. D 21, 2185 (1980).
  3. P. Candelas and K. W. Howard, Phys. Rev. D 29, 1618 (1984).
  4. P. R. Anderson, W. A. Hiscock, and D. A. Samuel, Phys. Rev. Lett. 70, 1739 (1993).
  5. P. R. Anderson, W. A. Hiscock, and D. A. Samuel, Phys. Rev. D 51, 4337 (1995).
  6. W. A. Hiscock, Phys. Rev. D 31, 3288 (1985).
  7. J. R. Gott III, Astrophys. J. 288, 422 (1985).
  8. B. Allen and A. C. Ottewill, Phys. Rev. D 42, 2669 (1990).
  9. M. Koike, X. Laquidain, and N. Graham, Phys. Rev. D 110, 105009 (2024).
  10. N. Graham, Phys. Rev. D 111, 105028 (2025).
  11. N. R. Khusnutdinov and M. Bordag, Phys. Rev. D 59, 064017 (1999).
  12. N. R. Khusnutdinov and A. R. Khabibullin, Gen. Relativ. Gravit. 36, 1613 (2004).
  13. K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer, New York, 1977).
  14. R. G. Newton, Scattering Theory of Waves and Particles (Springer, New York, 1982).
  15. N. Graham, R. Jaffe, V. Khemani, M. Quandt, M. Scandurra, and H. Weigel, Nucl. Phys. B645, 49 (2002).
  16. T. M. Helliwell and D. A. Konkowski, Phys. Rev. D 34, 1918 (1986).
  17. B. Linet, Phys. Rev. D 35, 536 (1987).
  18. V. P. Frolov and E. M. Serebriany, Phys. Rev. D 35, 3779 (1987).
  19. M. Bordag, J. Phys. A 28, 755 (1995).
  20. N. Graham and H. Weigel, Int. J. Mod. Phys. A 37, 2241004 (2022).
  21. M. F. Maghrebi, S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Proc. Natl. Acad. Sci. U.S.A. 108, 6867 (2011).
  22. N. Graham, Physics 5, 1003 (2023).
  23. F. Oberhettinger, Commun. Pure Appl. Math. 7, 551 (1954).
  24. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives (Gordon and Breach Science, Yverdon, Switzerland, 1993).

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Phys. Rev. D 114, 085004– Published 6 October, 2026
  • Received 4 August 2026
  • Accepted 11 September 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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