A new version of the background field formalism
offered recently by L. D. Faddeev will be
reported. External field  satisfies the quantum
equation of motion which coincides with the
classical one in the first order on the Planck
constant. Some results on equivalence of this
approach and the traditional QFT methods are
obtained (by the speaker and Yu.M. Pis'mak).
The last result constitutes the main part of
the speaker's Ph.D. thesis dedicated to the
application of this formalism to the
renormalization problem in the nonlinear sigma
model.