# Departmental Seminar

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

**Vladimir Bazhanov**

**Wednesday 23 October 2013 11.30am**

**Theoretical Physics seminar room, Le Couteur (Bldg #59), L.3.17**

**Prof Vladimir Bazhanov**

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 arises 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.