On the developments of Sklyanin's quantum separation of variables for integrable quantum field theories

Abstract

We present a microscopic approach in the framework of Sklyanin's quantum separation of variables (SOV) for the exact solution of 1+1-dimensional quantum field theories by integrable lattice regularizations. Sklyanin's SOV is the natural quantum analogue of the classical method of separation of variables and it allows a more symmetric description of classical and quantum integrability w.r.t. traditional Bethe ansatz methods. Moreover, it has the advantage to be applicable to a more general class of models for which its implementation gives a characterization of the spectrum complete by construction. Our aim is to introduce a method in this framework which allows at once to derive the spectrum (eigenvalues and eigenvectors) and the dynamics (time dependent correlation functions) of integrable quantum field theories (IQFTs). This approach is presented for a paradigmatic example of relativistic IQFT, the sine-Gordon model.Comment: 8 pages; invited contribution to the Proceedings of the XVIIth INTERNATIONAL CONGRESS ON MATHEMATICAL PHYSICS, August 2012, Aalborg, Danemark; accepted for publication on the ICMP12 Proceedings by World Scientific. The material here presented is strictly connected to that introduced in arXiv:0910.3173 and arXiv:1204.630