Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

NONRELATIVISTIC LIMIT IN THE SELF-DUAL ABELIAN CHERN-SIMONS MODEL

  • Han, Jong-Min (DEPARTMENT OF MATHEMATICS HANKUK UNIVERSITY OF FOREIGN STUDIES) ;
  • Song, Kyung-Woo (DEPARTMENT OF MATHEMATICS KYUNG HEE UNIVERSITY)
  • Published : 2007.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

We consider the nonrelativistic limit in the self-dual Abelian Chern-Simons model, and give a rigorous proof of the limit for the radial solutions to the self-dual equations with the nontopological boundary condition when there is only one-vortex point. By keeping the shooting constant of radial solutions to be fixed, we establish the convergence of radial solutions in the nonrelativistic limit.

Keywords

References

  1. D. Chae and O. Yu Imanuvilov, The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Comm. Math. Phys. 215 (2000), no. 1, 119-142 https://doi.org/10.1007/s002200000302
  2. H. Chan, C.-C. Fu, and C.-S. Lin, Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation, Comm. Math. Phys. 231 (2002), no. 2, 189-221 https://doi.org/10.1007/s00220-002-0691-6
  3. W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), no. 3, 615-622 https://doi.org/10.1215/S0012-7094-91-06325-8
  4. X. Chen, S. Hastings, J. B. McLeod, and Y. Yang, A nonlinear elliptic equation arising from gauge field theory and cosmology, Proc. Roy. Soc. London Ser. A 446 (1994), no. 1928, 453-478 https://doi.org/10.1098/rspa.1994.0115
  5. K. Choe, Uniqueness of the topological multivortex solution in the self-dual Chern-Simons theory, J. Math. Phys. 46 (2005), no. 1, 012305, 22pp
  6. G. V. Dunne, Self-dual Chern-Simons Theories, Springer, 1995
  7. J. Hong, Y. Kim, and P. Y. Pac, Multivortex Solutions of the Abelian Chern-Simons-Higgs Theory, Phys. Rev. Lett. 64 (1990), no. 19, 2230-2233 https://doi.org/10.1103/PhysRevLett.64.2230
  8. R. Jackiw and S.-Y. Pi, Soliton solutions to the gauged nonlinear Schrodinger equations on the plane, Phys. Rev. Lett. 64 (1990), no. 25, 2969-2972 https://doi.org/10.1103/PhysRevLett.64.2969
  9. R. Jackiw and S.-Y. Pi, Classical and quantal nonrelativistic Chern-Simons theory, Phys. Rev. D (3) 42 (1990), no. 10, 3500-3513 https://doi.org/10.1103/PhysRevD.42.3500
  10. R. Jackiw and E. J. Weinberg, Self-dual Chen-Simons Vortices, Phys. Rev. Lett. 64 (1990), 2234-2237 https://doi.org/10.1103/PhysRevLett.64.2234
  11. A. Jaffe and C. Taubes, Vortices and Monopoles, Birkhauser, Boston, 1980
  12. J. Parajapat and G. Tarantello, On a class of elliptic problems in $R^2$: symmetry and uniqueness results, Proc. Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), no. 4, 967-985 https://doi.org/10.1017/S0308210500001219
  13. J. Spruck and Y. Yang, The existence of nontopological solitons in the self-dual Chern-Simons theory, Comm. Math. Phys. 149 (1992), no. 2, 361-376 https://doi.org/10.1007/BF02097630
  14. J. Spruck and Y. Yang, Topological solutions in the self-dual Chern-Simons theory, Ann. Inst. Henri Poincare Anal. non Lineaire 12 (1995), no. 1, 75-97 https://doi.org/10.1016/S0294-1449(16)30168-8
  15. G. Tarantello, Selfdual Maxwell-Chern-Simons vortices, Milan J. Math. 72 (2004), 29-80 https://doi.org/10.1007/s00032-004-0030-9
  16. R. Wang, The Existence of Chern-Simons Vortices, Comm. Math. Phys. 137 (1991), no. 3, 587-597 https://doi.org/10.1007/BF02100279

Cited by

  1. Semi-nonrelativistic limit of the Chern–Simons–Higgs system vol.50, pp.7, 2009, https://doi.org/10.1063/1.3179159