Conservation laws in Skyrme-type models

被引:9
作者
Adam, C. [1 ]
Sanchez-Guillen, J.
Wereszczynski, A.
机构
[1] Univ Santiago de Compostela, Dept Fis Particulas, E-15782 Santiago De Compostela, Galicia, Spain
[2] Univ Santiago de Compostela, Inst Galego Fis Altas Enerxias, E-15782 Santiago De Compostela, Galicia, Spain
[3] Jagiellonian Univ, Inst Phys, PL-30059 Krakow, Poland
关键词
D O I
10.1063/1.2710652
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The zero curvature representation of Zakharov and Shabat [V. E. Zakharov and A. B. Shabat, Soviet Phys. JETP 34, 62 (1972)] has been generalized recently to higher dimensions and has been used to construct nonlinear field theories which are integrable or contain integrable submodels. The Skyrme model, for instance, contains an integrable subsector with infinitely many conserved currents, and the simplest Skyrmion with baryon number 1 belongs to this subsector. Here we use a related method, based on the geometry of target space, to construct a whole class of theories which are integrable or contain integrable subsectors (where integrability means the existence of infinitely many conservation laws). These models have three-dimensional target space, like the Skyrme model, and their infinitely many conserved currents turn out to be Noether currents of the volume-preserving diffeomorphisms on target space. Specifically for the Skyrme model, we find both weak and strong integrability conditions, where the conserved currents form a subset of the algebra of volume-preserving diffeomorphisms in both cases, but this subset is a subalgebra only for the weak integrable submodel.
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页数:16
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