Integrable structure of Quantum Field Theory: classical flat connections versus quantum stationary states
Integrable structure of Quantum Field Theory: classical flat connections versus quantum stationary states
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量子场论的可积结构：经典平面连接与量子稳态
DOI：
10.1007/jhep09(2014)147
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发表时间：
2013
影响因子：
5.4
通讯作者：
S. Lukyanov
中科院分区：
文献类型：
--
作者：
V. Bazhanov;S. Lukyanov
我们建立了（经典）修正sinh-Gordon方程的无限特解集与V.A.法捷耶夫在这种情况下，修改后的sinh-Gordon方程作为穿孔Riemann球面上一类多值联络的零曲率条件出现，类似于希钦的自对偶方程。建议之间的对应关系的经典和量子可积系统提供了一个强有力的工具，推导功能和积分方程，确定在有限体积的大规模QFT运动的局部积分的全谱。我们的结果的潜在应用问题的非微扰量子化的经典可积非线性西格玛模型进行了简要的讨论。
We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finite-volume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinh-Gordon equation arise in this case as a zero-curvature condition for a class of multivalued connections on the punctured Riemann sphere, similarly to Hitchin’s self-duality equations. The proposed correspondence between the classical and quantum integrable systems provides a powerful tool for deriving functional and integral equations which determine the full spectrum of local integrals of motion for massive QFT in a finite volume. Potential applications of our results to the problem of non-perturbative quantization of classically integrable non-linear sigma models are briefly discussed.