Hopf term, loop algebras and three dimensional Navier-Stokes equation
Hopf term, loop algebras and three dimensional Navier-Stokes equation
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Hopf 项、循环代数和三维纳维-斯托克斯方程
DOI：
10.1142/s0217732393003068
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
Y. Matsuo
中科院分区：
文献类型：
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作者：
Y. Matsuo
三维理想流体的动力学相当于涡流细丝或“弦”的运动。我们研究了它的作用原理，发现它可以用非线性Sigma模型的Hopf项来描述。Poisson括号结构由回路代数来描述，例如，Virasoro代数或类似于O(3)电流代数。作为一种弦理论，它与标准的Nambu-Goto弦在与外在几何的耦合上有很大的不同。我们还对二维情况进行了简要的分析，并对W1+∞结构作了一些重点介绍。
The dynamics of the three-dimensional perfect fluid is equivalent to the motion of vortex filaments or "strings." We study the action principle and find that it is described by the Hopf term of the nonlinear sigma model. The Poisson bracket structure is described by the loop algebra, for example, the Virasoro algebra or the analog of O(3) current algebra. As a string theory, it is quite different from the standard Nambu-Goto string in its coupling to the extrinsic geometry. We also analyze briefly the two-dimensional case and give some emphasis on the w1+∞ structure.