On the Integrability of the Bukhvostov–Lipatov Model

The integrability of the Bukhvostov–Lipatov four-fermion model is investigated. It is shown that the classical model possesses a current of Lorentz spin 3, conserved both in the bulk and on the half-line for specific types of boundary actions. It is then established that the conservation law is spoiled at the quantum level — a fact that might indicate that the quantum Bukhvostov–Lipatovmodel is not integrable, contrary to what was previously believed.