It is shown that the symmetry under parity of the wavefunctions of two identical particles with an arbitrary spin
s in three spatial dimensions accounts for the appropriate wavefunction exchange statistics under the permutations of particles. The standard properties of the angular momentum in non-relativistic quantum mechanics account for the sign factor
(−1)2s that the wavefunctions acquire under the permutation of coordinates of the two particles, without any additional requirements, directly relating spin and the particle exchange statistics in the non-relativistic context.
We study the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a spacetime lattice using the worldline formulation. By tuning the chemical potential carefully we show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector. Since fermions can be treated as hard-core bosons up to a permutation sign, we also apply this approach to non-relativistic fermions. The fermion permutation sign is treated as an observable in this approach and can be used to extract energies for each particle-number sector. Since in one dimension non-relativistic fermions can only permute due to boundary effects, unlike the auxiliary field method, in many cases our approach does not suffer from sign problems. Using our method we discover limitations of the recently proposed complex Langevin calculations in one dimension.