Integrable structures in quantum field theory (Q2818225)

This paper provides a review and overview of the algebraic underpinnings of integrable structures in field theories. It presents the work of \textit{V. V. Bazhanov} et al. [Commun. Math. Phys. 177, No. 2, 381--398 (1996; Zbl 0851.35113); Commun. Math. Phys. 190, No. 2, 247--278 (1997; Zbl 0908.35114); Commun. Math. Phys. 200, No. 2, 297--324 (1999; Zbl 1057.81531); Nucl. Phys., B 489, No. 3, 487--531 (1997; Zbl 0925.81325)] in a uniform way that aims to be accessible to students and non-experts.NEWLINENEWLINEThe paper begins with an overview of conformal field theories as examples of massless integrable field theories and introduces the concepts of transfer matrices, Baxter \(Q\)-operators, thermodynamic Bethe ansatz and nonlinear integrals of motion in this simplified case.NEWLINENEWLINEThis notions are then extended to massive field theories by considering massive deformations of conformal field theories. The paper concludes with the ODE/IM correspondence, which is presented in the example of the sine-Gordon model.