Schwinger-Dyson analysis of an exactly solvable model

I present an exactly solvable quantum field theory in 0+1 dimensions in which a fermion field interacts with a boson field via a Yukawa coupling. The exact two-point Green's functions are constructed and compared with the Green's functions obtained from a ladder approximation to the Schwinger-Dyson equations. I find that the ladder approximation fails to produce even a qualitative agreement with the exact spectral function except in the weak-coupling limit.