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

Giuliano Niccoli (C. N. Yang Institute, Stony Brook)

Tuesday 25th September, 2012 15:00-16:00 326


The exact solution of quantum field theories (QFTs) by the complete characterization of their spectrum and dynamics (correlation functions) remains still one fundamental open problem in mathematical physics, of great interest as it should lead to non-perturbative results in several areas of physics where these models play a central role. Here, we present a microscopic approach aimed to simultaneously characterize the spectrum and the dynamics for the class of 1+1-dimensional QFTs with integrable lattice regularizations analyzable by Sklyanin's quantum separation of variables (SOV). 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 large class of models for which its implementation gives a characterization of the spectrum complete by construction. Our approach is presented for a paradigmatic example of relativistic integrable QFT, the sine-Gordon model. The results for both the spectrum and the dynamics of its lattice regularization will be presented and the beautiful feature of universality, emerging from the comparison with the results of other key integrable quantum models, will be pointed out.

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