The standard correspondence principle implies that quantum theory reduces to classical theory in the limit of the vanishing Planck constant. This project is devoted to a new type connection between quantum and classical systems which holds for arbitrary finite values of the Planch constant. The connection relates integrable quantum field theory (QFT) with integrable classical non-linear evolution equations in two space-time dimensions. More precisely there is a one-to-one correspondence between stationary states in the quantum theory and singular solutions of the classical evolution equations.
At the honours level the project will consist of a basic introduction into integrable quantum (classical) field theory in two dimensions (2D).
At the Masters and PhD levels the project will aim to apply this connection to study some important models of 2D QFT, in particular, the so-called non-linear sigma models. The required techniques range from the spectral theory of differential equations and theory of integrable quantum systems to numerical analysis of partial differential equations on the super-computer.
- Vladimir V. Bazhanov, Sergei L. Lukyanov, "Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states", arXiv:1310.4390
- V Rubakov, Classical Theory of Gauge Fields, Princeton University Press, 2002.