We consider a remarkable relation between the spectral theory of Ordinary Differential Equations (ODE) and Integrable Quantum Field Theory (IQFT) in two space-time dimensions. On the example of the Thirring field theory we show that the stationary states of the quantum model are in one-to-one correspondence with a family of Schrodinger operators. This is, in fact, part of a general phenomenon which relates the theory of differential equations and integrable quantum field theory and goes by the name of the ODE/IQFT correspondence. In our recent work we used this correspondence as the basis of a new approach to integrable quantum field theory. We applied this approach to non-linear sigma models which are difficult to analyze using established methods, yet have important applications in various branches of physics ranging from condensed matter to string theory. We present and discuss some of our latest results in this area.

Gleb Kotousov is a PhD student at the Department of Theoretical Physics supervised by Professor Vladimir Bazhanov.