From the Superparticle Path Integral to Superfield Theory

We investigate the hitherto unexplored relation between the superparticle path integral and superfield theory. Requiring that the path integral has the global symmetries of the classical action and obeys the natural composition property of path integrals, and also that the discretized action has the correct naive continuum limit, we find a viable discretization of the (D=3,N=2) free superparticle action. The resulting propagator is not the usual superfield one. We extend the discretization to include the coupling to an external gauge supermultiplet and use this to show the equivalence to superfield theory. This is possible since we are able to reformulate the superfield perturbation theory in terms of our new propagator.