Research PapersNo Access

TOPOLOGICAL OBJECTS IN THE O(3) NONLINEAR SIGMA MODEL

PENG-MING ZHANG

Institute of Modern Physics, Chinese Academy of Sciences, P. O. Box 31, Lanzhou 730000, P. R. China

Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, P. R. China

Corresponding author.

Search for more papers by this author

XI-GUO LEE

Institute of Modern Physics, Chinese Academy of Sciences, P. O. Box 31, Lanzhou 730000, P. R. China

Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, P. R. China

Search for more papers by this author

SHAO-FENG WU

College of Science, Shanghai University, Shanghai 200444, P. R. China

Search for more papers by this author

, and

YI-SHI DUAN

Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S021773230702244XCited by:0 (Source: Crossref)

Abstract

We study the topological defects in the nonlinear O(3) sigma model in terms of the decomposition of U(1) gauge potential. Time-dependent baby skyrmions are discussed in the (2+1)-dimensional spacetime with the CP¹ field. Furthermore, we show that there are three kinds of topological defects–vortex lines, point defects and knot exist in the (3+1)-dimensional model, and their topological charges, locations and motions are determined by the ϕ-mapping topological current theory.

Keywords:

PACS: 11.10.Lm, 05.45.Yv, 02.10.Kn

References

R. Rajaraman , Solitons and Instantons ( North-Holland , 1989 ) . Google Scholar
G. Morandi , The Role of Topology in Classical and Quantum Physics ( Springer-Verlag , 1992 ) . Crossref, Google Scholar
T. Tsurumaru and I. Tsutsui, Phys. Letts. B 460, 94 (1999), DOI: 10.1016/S0370-2693(99)00740-6. Crossref, Web of Science, ADS, Google Scholar
M. Kimura, H. Kobayashi and I. Tsutsui, Nucl. Phys. B 527, 624 (1998), DOI: 10.1016/S0550-3213(98)00389-7. Crossref, Web of Science, ADS, Google Scholar
E. Fradkin , Field Theories of Condensed Matter Systems ( Addison-Wesley , 1991 ) . Google Scholar
A. A. Belavin and A. M. Polyakov, JETP Lett. 22, 245 (1975). Web of Science, ADS, Google Scholar
F. Wilczek and A. Zee, Phys. Rev. Lett. 51, 2250 (1983), DOI: 10.1103/PhysRevLett.51.2250. Crossref, Web of Science, ADS, Google Scholar
E. Witten, Nucl. Phys. B 223, 433 (1983), DOI: 10.1016/0550-3213(83)90064-0. Crossref, Web of Science, ADS, Google Scholar
A. M. Tsvelik , Quantum Field Theory in Condensed Matter ( Cambridge Univ. Press , 1995 ) . Google Scholar
Y. S. Duan, G. H. Yang and Y. Jiang, Gen. Rel. Grav. 29, 715 (1997), DOI: 10.1023/A:1018881821774. Crossref, Web of Science, ADS, Google Scholar
Y. S. Duan and M. L. Ge, Sci. Sin. 11, 1072 (1979). Google Scholar
Y. S. Duan, H. Zhang and S. Li, Phys. Rev. B 58, 125 (1998), DOI: 10.1103/PhysRevB.58.125. Crossref, Web of Science, ADS, Google Scholar
P. M. Zhanget al., Phys. Lett. A 326, 375 (2004), DOI: 10.1016/j.physleta.2004.04.060. Crossref, Web of Science, ADS, Google Scholar
P. M. Zhang, Y. S. Duan and L. M. Cao, Mod. Phys. Lett. A 18, 2587 (2003), DOI: 10.1142/S021773230301209X. Link, Web of Science, ADS, Google Scholar
J. A. Schouten , Tensor Analysis for Physicists ( Clarendon , 1951 ) . Google Scholar
H. J. de Vega, Phys. Rev. D 18, 2945 (1978), DOI: 10.1103/PhysRevD.18.2945. Crossref, Web of Science, Google Scholar
J. Milnor , Topology from the Differential Viewpoint ( University of Virginia , 1966 ) . Google Scholar
Y. S. Duan, H. Zhang and L. B. Fu, Phys. Rev. E 59, 528 (1999), DOI: 10.1103/PhysRevE.59.528. Crossref, Web of Science, ADS, Google Scholar
H. K. Moffatt, J. Fluid. Mech. 35, 117 (1969), DOI: 10.1017/S0022112069000991. Crossref, Web of Science, ADS, Google Scholar
L. Faddeev and A. J. Niemi, Nature 387, 58 (1997), DOI: 10.1038/387058a0. Crossref, Web of Science, ADS, Google Scholar
T. Eguchi, P. B. Gilkey and A. J. Hanson, Phys. Rep. 66, 213 (1980), DOI: 10.1016/0370-1573(80)90130-1. Crossref, Web of Science, ADS, Google Scholar
C. Nash and S. Sen , Topology and Geometry of Physicists ( Academic Press , 1983 ) . Google Scholar
E. Witten, Commun. Math. Phys. 121, 351 (1989), DOI: 10.1007/BF01217730. Crossref, Web of Science, ADS, Google Scholar
Y. S. Duan, X. Liu and L. B. Fu, Phys. Rev. D 67, 085022 (2003), DOI: 10.1103/PhysRevD.67.085022. Crossref, Web of Science, Google Scholar