Quantum field theory, Grassmannians, and algebraic curves
Quantum field theory, Grassmannians, and algebraic curves
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量子场论、格拉斯曼方程和代数曲线
DOI：
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发表时间：
1988
期刊：
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通讯作者：
E. Witten
中科院分区：
文献类型：
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作者：
E. Witten
本文致力于阐明量子场论与无限格拉斯曼方程之间关系的某些方面，并指出黎曼曲面上的共形场论与现代自守表示理论之间存在着密切的类比。在此过程中，我们开发了当前代数中常见的加法沃德恒等式的乘法模拟。我们还根据算子值微分形式的留数，以一种可能有用的方式重新表述了加性 Ward 恒等式。结论部分专门讨论了弦场论的一些评论。在附录中，我们试图澄清 Beilinson、Manin 和 Schechtman 最近对所谓的全局 Virasoro 代数的构造。
This paper is devoted in part to clarifying some aspects of the relation between quantum field theory and infinite Grassmannians, and in part to pointing out the existence of a close analogy between conformal field theory on Riemann surfaces and the modern theory of automorphic representations. Along the way we develop a multiplicative analog of the usual additive Ward identities of current algebra. We also reformulate the additive Ward identities in a way which may be useful, in terms of the residues of operator-valued differential forms. A concluding section is devoted to some remarks on string field theory. In an appendix, we attempt to clarify the recent construction by Beilinson, Manin, and Schechtman of what might be called global Virasoro algebras.