  Ultracold atomic gases are, to a very good approximation, described by
pairwise zero-range interactions. This paper demonstrates that $N$-body systems
with two-body zero-range interactions can be treated reliably and efficiently
by the finite temperature and ground state path integral Monte Carlo
approaches, using the exact two-body propagator for zero-range interactions in
the pair product approximation. Harmonically trapped one- and three-dimensional
systems are considered. A new propagator for the harmonically trapped two-body
system with infinitely strong zero-range interaction, which may also have
applications in real time evolution schemes, is presented.
