  We construct contact interactions for bosonic and fermionic point particles.
We first relate the resulting theories to classical electrostatics by taking
functional averages over worldlines whose endpoints are fixed to charged
particles. Counting those paths which pass through a space-time point $x^{\mu}$
gives the static electric field at that point, provided we take the limit where
the length measured along the worldlines is large. We also investigate
corrections to the classical field that arise beyond leading order in this
limit before constructing a theory of point particles that interact when their
worldlines intersect. We quantise this theory and show that the partition
function contains propagator couplings between the endpoints of the particles
before discussing how this is related to the worldline formalism of quantum
field theory and general action at a distance theories.
