Quantization of Open Toda Lattices
Quantization of Open Toda Lattices
复制标题
开 Toda 格子的量化
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
M. Semenov
中科院分区：
文献类型：
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作者：
M. Semenov
在上一章中，我们描述了开Toda格的几何实现。Kostant[1979]已经在他的第一篇关于这个主题的论文中指出了几何方案对量子Toda晶格的扩展。大约在同一时间(1978-1981)，一种强大而复杂的量子逆散射方法被创造出来，用于研究量子可积系统(见Faddeev[1980,1984])。正如人们很快意识到的，它超越了李群和李代数的普通理论，并引入了量子群的新概念(Drinfel‘d[1987])。从这个一般观点来看，量子Kostant-Adler方案是某种极限情况，它对应于基本对易关系的线性化。[应该记住，量子逆散射法的基本对易关系是二次的；它们可以被视为上一章第12节中考虑的二次泊松括号关系的量子化。]
In the previous chapter we described a geometric realization of open Toda lattices. Already in his first paper on the subject Kostant [1979] indicated an extension of geometrical scheme to quantum Toda lattices. About the same time (1978–1981), a powerful and sophisticated technique of the Quantum Inverse Scattering Method was created for the study of quantum integrable systems (see Faddeev [1980, 1984]). As was soon realized, it goes beyond the ordinary theory of Lie groups and Lie algebras and introduces the new notion of quantum groups (Drinfel’d [1987]). From this general point of view the ‘quantum Kostant-Adler scheme’ is a certain limiting case which corresponds to linearization of the basic commutation relations. [It should be recalled that the basic commutation relations of the Quantum Inverse Scattering Method are quadratic; they may be regarded as the quantization of quadratic Poisson bracket relations considered in Section 12 of the previous chapter.]