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We formulate the physics of two species of non-relativistic hard-core bosonswith attractive or repulsive delta function interactions on a space-timelattice in the worldline approach. We show that worm algorithms can efficientlysample the worldline configurations in any fixed particle-number sector if thechemical potential is tuned carefully. Since fermions can be treated ashard-core bosons up to a permutation sign, we apply this approach to studynon-relativistic fermions. The fermion permutation sign is an observable inthis approach and can be used to extract energies in each particle-numbersector. In one dimension, non-relativistic fermions can only permute acrossboundaries, and so our approach does not suffer from sign problems in manycases, unlike the auxiliary field method. Using our approach, we discoverlimitations of the recently proposed complex Langevin calculations in onespatial dimension for some parameter regimes. In higher dimensions, our methodsuffers from the usual fermion sign problem. Here we provide evidence that itmay be possible to alleviate this problem for few-body physics

Few-body physics on a space-time lattice in the worldline approach