  We develop a nonperturbative method to calculate the electron propagator in
low-dimensional and strongly correlated electron systems. The method builds on
our earlier work using a Hubbard-Stratonovich transformation to map the
tunneling problem to the x-ray edge problem, which accounts for the infrared
catastrophe caused by the sudden introduction of a new electron into a
conductor during a tunneling event. Here we use a cumulant expansion to include
fluctuations about this x-ray edge limit. We find that the dominant effect of
electron-electron interaction at low energies is to correct the noninteracting
Green's function by a factor exp(-S), where S can be interpreted as the
Euclidean action for a density field describing the time-dependent charge
distribution of the newly added electron. Initially localized, this charge
distribution spreads in time as the electron is accommodated by the host
conductor, and during this relaxation process action is accumulated according
to classical electrostatics with a screened interaction. The theory applies to
lattice or continuum models of any dimensionality, with or without
translational invariance. In one dimension the method correctly predicts a
power-law density of states (DOS) for electrons with short-range interaction
and no disorder, and when applied to the solvable Tomonaga-Luttinger model, the
exact DOS is obtained.
