  We present an exact single-electron picture that describes the correlated
electron dynamics in strong laser fields. Our approach is based on the
factorization of the electronic wavefunction as a product of a marginal and a
conditional amplitude. The marginal amplitude, which depends only on one
electronic coordinate and yields the exact one-electron density and current
density, obeys a time-dependent Schr\"odinger equation with an effective
time-dependent potential. The exact equations are used to derive an
approximation that is a step towards a general and feasible ab-initio
single-electron approximation for molecules. The derivation also challenges the
usual interpretation of the single-active electron approximation. From the
study of model systems, we find that the exact and approximate single-electron
potentials for processes with negligible two-electron ionization lead to a
qualitatively similar dynamics, but that the ionization barrier may be
explicitly time-dependent.
