The propagator D for a particle is basically the Green's function of the differential operator that describes that particle, e.g. [tex] (\partial^2 + m^2) D(x-y) = \delta^4 (x-y). [/tex] This propagator is supposed to give the probability of the particle propagating from [itex]x[/itex] to [itex]y[/itex]. Why does this make sense? Why would the inverse of the differential operator have something to do with probabilities?