Integrability in classical and quantum field theory and the Bukhvostov-Lipatov model

A brief overview of the notions of classical and quantum integrability in 1+1 space-time dimensions is given with an emphasis on the existence of infinite number of conserved quantities in (1+1)D field theories. Some methods for building such conserved quantities are outlined and are then applied to study the integrability of the Bukhvostov-Lipatov model, a 2-field generalization of the sine-Gordon/massive Thirring model. The integrability properties of both the classical/quantum and the bosonic/fermionic versions of the model are discussed. It is shown that the classical fermionic model possesses a conserved current of Lorentz spin 3. It is then established that the conservation law is spoiled at the quantum level--a fact that indicates that the quantum Bukhvostov-Lipatov model is not integrable