Theoretical and Mathematical Physics

, Volume 191, Issue 3, pp 827–835 | Cite as

Electrodynamics with charged strings

  • A. B. Pestov


We show that in a four-dimensional space–time a complex scalar field can be associated with a one-dimensionally extended object, called a charged string. The string is said to be charged because the complex scalar field describing it interacts with an electromagnetic field. A charged string is characterized by an extension of the symmetry group of the charge space to a group of stretch rotations. We propose relativistically invariant and gauge-invariant equations describing the interaction of a complex scalar field with an electromagnetic field, and each solution of them corresponds to a charged string. We achieve this by introducing the notion of a charged string index, which, as verified, takes only integer values. We establish equations from which it follows that charged strings fit naturally into the framework of the Maxwell–Dirac electrodynamics.


electrodynamics magnetic charge anion string charged string 


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  1. 1.
    P. A. M. Dirac, “Quantised singularities in the electromagnetic field,” Proc. Roy. Soc. London Ser. A, 133, 60–72 (1931).ADSCrossRefMATHGoogle Scholar
  2. 2.
    F. Wilczek, “Two applications of axion electrodynamics,” Phys. Rev. Lett., 58, 1799–1802 (1987).ADSCrossRefGoogle Scholar
  3. 3.
    G. ’t Hooft, “Magnetic monopoles in unified gauge theories,” Nucl. Phys. B, 79, 276–284 (1974).ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    T. T. Wu and C. N. Yang, “Concept of nonintegrable phase factors and global formulation of gauge fields,” Phys. Rev. D, 12, 3845–3857 (1975).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Z. F. Ezawa, Quantum Hall Effects, World Scientific, Singapore (2000).CrossRefMATHGoogle Scholar
  6. 6.
    E. A. Kochetov and V. A. Osipov, “Gauge theory of disclinations on fluctuating elastic surfaces,” J. Phys. A: Math. Gen., 32, 1961–1972 (1999).ADSMathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    V. A. Osipov, “Topological defects in carbon nanocrystals,” in: Topology in Condensed Matter (Springer Ser. Solid State Sci., Vol. 150, M. I. Monastyrsky, ed.), Springer, Berlin (2006), pp. 93–116.CrossRefGoogle Scholar
  8. 8.
    M. Tajmar, “Electrodynamics in superconductors explained by Proca equations,” Phys. Lett. A, 372, 3289–3291 (2008).ADSCrossRefMATHGoogle Scholar
  9. 9.
    A. Vilenkin, “Cosmic strings and domain walls,” Phys. Rep., 121, 263–315 (1985).ADSMathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    E. Witten, “Superconducting strings,” Nucl. Phys. B, 249, 557–592 (1985).ADSCrossRefGoogle Scholar
  11. 11.
    V. V. Nesterenko and I. G. Pirozhenko, “Vacuum energy in conical space with additional boundary conditions,” Class. Q. Grav., 28, 175020 (2011).ADSMathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    B. M. Barbashov and V. V. Nesterenko, Introduction to the Relativistic String Theory, World Scientific, Singapore (1990).CrossRefMATHGoogle Scholar
  13. 13.
    H. B. Nielsen and P. Olesen, “Vortex-line models for dual strings,” Nucl. Phys. B, 61, 45–61 (1973).ADSCrossRefGoogle Scholar
  14. 14.
    F. Wilczek, “Magnetic flux, angular momentum, and statistics,” Phys. Rev. Lett., 48, 1144–1145 (1982).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Joint Institute for Nuclear ResearchDubna, Moscow OblastRussia

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