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We develop a nonperturbative method to calculate the electron propagator inlow-dimensional and strongly correlated electron systems. The method builds onour earlier work using a Hubbard-Stratonovich transformation to map thetunneling problem to the x-ray edge problem, which accounts for the infraredcatastrophe caused by the sudden introduction of a new electron into aconductor during a tunneling event. Here we use a cumulant expansion to includefluctuations about this x-ray edge limit. We find that the dominant effect ofelectron-electron interaction at low energies is to correct the noninteractingGreen's function by a factor exp(-S), where S can be interpreted as theEuclidean action for a density field describing the time-dependent chargedistribution of the newly added electron. Initially localized, this chargedistribution spreads in time as the electron is accommodated by the hostconductor, and during this relaxation process action is accumulated accordingto classical electrostatics with a screened interaction. The theory applies tolattice or continuum models of any dimensionality, with or withouttranslational invariance. In one dimension the method correctly predicts apower-law density of states (DOS) for electrons with short-range interactionand no disorder, and when applied to the solvable Tomonaga-Luttinger model, theexact DOS is obtained.Comment: 8 pages, Revte

Infrared catastrophe and tunneling into strongly correlated electron systems: Beyond the x-ray edge limit