Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method
Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method
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发表时间：
1978-06
影响因子：
1.1
通讯作者：
V. Zakharov;A. Mikhailov
中科院分区：
文献类型：
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作者：
V. Zakharov;A. Mikhailov
提出了一种方法推导和分类相对论不变的可积系统，是足够一般的，包括所有目前已知的二维可解模型，并为建设一些新的。本文引入的“规范等价”概念使人们能够澄清经典场论中几种不同模型之间的关系，如n场、sine-Gordon方程和Thirring模型。本文研究了SU（N）群的主手征场模型。结果表明，在N=3，该模型表现出非平凡的相互作用：衰变，融合和共振散射的孤子。提出了新的手征模型，场取李群的齐次空间中的值，并表现出高度的对称性。当齐次空间是格拉斯曼流形时，我们证明了这些模型的可积性。
A method is proposed for deriving and classifying relativistically invariant integrable systems that are sufficiently general to encompass all presently known two-dimensional solvable models, and for the construction of a few new ones. The concept of ''gauge equivalence'' introduced in this paper allows one to clarify the relation between several different models of classical field theory, such as the n-field, the sine-Gordon equation, and the Thirring model. We study the model of the principal chiral field for the group SU (N). It is shown that at N=3 this model exhibits nontrivial interactions: decay, fusion and resonant scattering of solitons. New chiral models are proposed with fields taking values in homogeneous spaces of Lie groups and exhibiting a high degree of symmetry. We prove the integrability of these models when the homogeneous space is a Grassmann manifold.