|
|
|
|
References
|
|
| |
| 1. |
Auckly D., Kapitanski L., “Holonomy and Skyrme's model”, Comm. Math. Phys., 240 (2003), 97–122     |
| 2. |
Auckly D., Kapitanski L., “Analysis of $S^2$-valued maps and Faddeev's model”, Comm. Math. Phys., 256 (2005), 611–620 |
| 3. |
Auckly D., Kapitanski L., The Pontrjagin–Hopf invariants for Sobolev maps, submitted |
| 4. |
Auckly D., Kapitanski L., Integrality of homotopy invariants in the Skyrme model, in preparation |
| 5. |
Auckly D., Speight J. M., Fermionic quantization and configuration spaces for the Skyrme and Faddeev–Hopf models, preprint, http://arxiv.org/abs/hep-th/0411010 |
| 6. |
Balachandran A., Marmo G., Skagerstam B., Stern A., Classical topology and quantum states, World Sci. Publ. Co., Inc., River Edge, NJ, 1991 |
| 7. |
Battye R. A., Sutcliffe P. M., “Skyrmions, fullerenes and rational maps”, Rev. Math. Phys., 14 (2002), 29–85 |
| 8. |
Bopp F., Haag Z., “Über die Möglichkeit von Spinmodellen”, Z. Naturforschung, 5a (1950), 644–653 |
| 9. |
Bott R., Tu L. W., Differential forms in algebraic topology, Grad. Texts is Math., 82, Springer-Verlag, New York–Berlin, 1982 |
| 10. |
Brezis H., “The interplay between analysis and topology in some nonlinear PDE problems”, Bull. Amer. Math. Soc. (N.S.), 40 (2003), 179–201 |
| 11. |
Dirac P., “The theory of magnetic poles”, Phys. Rev. (2), 74 (1948), 817–830 |
| 12. |
Faddeev L. D., Quantization of solitons, Preprint IAS print-75-QS70, 1975 |
| 13. |
Faddeev L. D., “Knotted solitons and their physical applications”, Topological Methods in the Physical Sciences (London, 2000), R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 359, 2001, 1399–1403 |
| 14. |
Faddeev L. D., Niemi A. J., “Stable knot-like structures in classical field theory”, Nature, 387 (1997), 58–61 |
| 15. |
Federer H., “A study of function spaces by spectral sequences”, Trans. Amer. Math. Soc., 82 (1956), 340–361 |
| 16. |
Finkelstein D., Rubinstein J., “Connection between spin, statisitics, and kinks”, J. Math. Phys., 9 (1968), 1762–1779 |
| 17. |
Gisiger T., Paranjape M. B., “Recent mathematical developments in the Skyrme model”, Phys. Rep., 306:3 (1998), 109–211 |
| 18. |
Giulini D., “On the possibility of spinorial quantization in the Skyrme model”, Modern Phys. Lett. A, 8 (1993), 1917–1924 |
| 19. |
Hansen V. L., http://www.mat.dtu.dk/people/V.L.Hansen/string.html |
| 20. |
Hietarinta J., Salo P., “Ground state in the Faddeev–Skyrme model”, Phys. Rev. D, 62 (2000), 081701(R) |
| 21. |
Kapitanski L., “On Skyrme's model”, Nonlinear Problems in Mathematical Physics and Related Topics, II, Int. Math. Ser. (N.Y.), 2, Kluwer/Plenum, New York, 2002, 229–241 |
| 22. |
Kirby R. C., The topology of 4-manifolds, Lecture Notes in Math., 1374, Springer-Verlag, Berlin, 1989 |
| 23. |
Koshkin S., Homogeneous spaces and Faddeev–Skyrme models, Dissertation, Kansas State Univ., 2006 |
| 24. |
Mandl F., Shaw G., Quantum field theory, Wiley, 1991 |
| 25. |
Pontrjagin L., “A classification of mappings of the three-dimensional complex into the two-dimensional sphere”, Mat. sb., 9(51):2 (1941), 331–363  |
| 26. |
Rajaraman R., Solitons and instantons, North-Holland, Amsterdam, 1982 |
| 27. |
Schulman L., “A path integral for spin”, Phys. Rev. (2), 176 (1968), 1558–1569 |
| 28. |
Simms D. J., Woodhouse N. M. J., Lectures in geometric quantization, Lecture Notes in Phys., 53, Springer-Verlag, Berlin–New York, 1976 |
| 29. |
Skyrme T. H. R., “A unified field theory of mesons and baryons”, Nuclear Phys., 31 (1962), 556–569 |
| 30. |
Sorkin R., “A general relation between kink-exchange and kink-rotation”, Comm. Math. Phys., 115 (1988), 421–434 |
| 31. |
Vakulenko A. F., Kapitanskii L. V., “Ustoichivost solitonov v $S^2$-nelineinoi $\sigma$-modeli”, Dokl. AN SSSR, 246:4 (1979), 840–842 |
| 32. |
Weinberg S., The quantum theory of fields, vol. 1, Cambridge Univ. Press, Cambridge, 1996 |
| 33. |
White B., “Homotopy classes in Sobolev spaces and the existence of energy minimizing maps”, Acta Math., 160 (1988), 1–17 |
| 34. |
Witten E., “Current algebra, baryons, and quark confinement”, Nuclear Phys. B, 233 (1983), 433–444 |
| 35. |
Zaccaria F., Sudarshan E., Nilsson J., Mukunda N., Marmo G., Balachandran A., “Universal unfolding of Hamiltonian systems: from symplectic structure to fiber bundles”, Phys. Rev. D (3), 27 (1983), 2327–2340 |
