Connecting spin and statistics in quantum mechanics

TL;DR

This paper presents a straightforward derivation of the spin-statistics connection in quantum mechanics, relying on simple postulates and rotational exchanges, applicable in both Galilean and relativistic contexts without quantum field theory.

Contribution

It offers a novel, simplified derivation of the spin-statistics relation using basic assumptions and rotational exchanges, avoiding the complexities of quantum field theory.

Findings

The derivation applies to both Galilean and Lorentz-invariant quantum mechanics.

The spin factor (-1)^{2s} is shown to belong to the exchange wave function.

The method controls spinor ambiguity through azimuthal angle exchange via rotations.

Abstract

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (-1)^2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required.