  We develop an efficient method to calculate the third-order corrections to
the self-energy of the hole-doped two-dimensional Hubbard model in space-time
representation. Using the Dyson equation we evaluate the renormalized spectral
function in various parts of the Brillouin zone and find significant
modifications with respect to the second-order theory even for rather small
values of the coupling constant U. The spectral function becomes unphysical for
$ U \simeq W $, where W is the half-width of the conduction band. Close to the
Fermi surface and for U<W, the single-particle spectral weight is reduced in a
finite energy interval around the Fermi energy. The increase of U opens a gap
between the occupied and unoccupied parts of the spectral function.
