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arXiv · 1310.4390

Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states

Vladimir V. Bazhanov·Sergei L. Lukyanov
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Abstract

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 of 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.

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Vladimir V. Bazhanov, Sergei L. Lukyanov. 2013-10-16. Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states. https://doi.org/10.1007/jhep09(2014)147

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