  We give a non-perturbative construction of the fermionic projector in
Minkowski space coupled to a time-dependent external potential which is smooth
and decays faster than quadratically for large times. The weak and strong mass
oscillation properties are proven. We show that the integral kernel of the
fermionic projector is of Hadamard form, provided that the time integral of the
spatial sup-norm of the potential satisfies a suitable bound. This gives rise
to an algebraic quantum field theory of Dirac fields in an external potential
with a distinguished pure quasi-free Hadamard state.
