The following is a list of references on the construction of Skyrmion-solutions of the Yang-Mills field via rational maps from the complex plane, hence holomorphic maps from the Riemann sphere, to itself, akin to the Donaldson-construction of Yang-Mills monopoles.
The original idea:
Further discussion:
Steffen Krusch, Skyrmions and the Rational Map Ansatz, Nonlinearity 13:2163, 2000 (arXiv:hep-th/0006147)
Nicholas S. Manton, Bernard M.A.G. Piette, Understanding Skyrmions using Rational Maps, in: Casacuberta C., Miró-Roig R.M., Verdera J., Xambó-Descamps S. (eds.) European Congress of Mathematics. Progress in Mathematics, vol 201. Birkhäuser, Basel. 2001 (doi:10.1007/978-3-0348-8268-2_27, arXiv:hep-th/0008110)
Richard Battye, Paul Sutcliffe, Skyrmions, Fullerenes and Rational Maps, Rev. Math. Phys. 14 (2002) 29-86 (arXiv:hep-th/0103026)
W.T. Lin, Bernard M.A.G. Piette, Skyrmion Vibration Modes within the Rational Map Ansatz, Phys. Rev. D77:125028, 2008 (arXiv:0804.4786, doi:10.1103/PhysRevD.77.125028)
L. A. Ferreira, L. R. Livramento: Harmonic, Holomorphic and Rational Maps from Self-Duality [arXiv:2412.02636]
On quantization of Skyrmions informed by homotopy of rational maps:
Steffen Krusch, Homotopy of rational maps and the quantization of Skyrmions, Annals of Physics Volume 304, Issue 2, April 2003, Pages 103-127 (doi:10.1016/S0003-4916(03)00014-9, arXiv:hep-th/0210310)
Steffen Krusch, Skyrmions and Rational Maps, talk at KIAS 2004 (pdf, pdf)
Steffen Krusch, Quantization of Skyrmions (arXiv:hep-th/0610176)
the impact of which, on the computation of atomic nuclei, is highlighted in:
See also:
Last revised on April 11, 2025 at 06:29:55. See the history of this page for a list of all contributions to it.