  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-Lipatov model is not integrable, contrary to what was previously
believed.
