  We formulate the physics of two species of non-relativistic hard-core bosons
with attractive or repulsive delta function interactions on a space-time
lattice in the worldline approach. We show that worm algorithms can efficiently
sample the worldline configurations in any fixed particle-number sector if the
chemical potential is tuned carefully. Since fermions can be treated as
hard-core bosons up to a permutation sign, we apply this approach to study
non-relativistic fermions. The fermion permutation sign is an observable in
this approach and can be used to extract energies in each particle-number
sector. In one dimension, non-relativistic fermions can only permute across
boundaries, and so our approach does not suffer from sign problems in many
cases, unlike the auxiliary field method. Using our approach, we discover
limitations of the recently proposed complex Langevin calculations in one
spatial dimension for some parameter regimes. In higher dimensions, our method
suffers from the usual fermion sign problem. Here we provide evidence that it
may be possible to alleviate this problem for few-body physics
