Parity as the foundation of the non-relativistic spin-statistics connection

TL;DR

This paper demonstrates that parity symmetry in non-relativistic quantum mechanics explains the spin-statistics connection for identical particles, linking wavefunction symmetry and particle exchange without extra assumptions.

Contribution

It shows that parity symmetry alone accounts for the spin-dependent exchange statistics of identical particles in non-relativistic quantum mechanics.

Findings

Parity symmetry explains the wavefunction exchange statistics.

The sign factor $(-1)^{2s}$ arises naturally from angular momentum properties.

No additional assumptions are needed for the spin-statistics relation.

Abstract

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.