Quantal statistical phase factor accompanying inter-change of two particles

TL;DR

This paper demonstrates that particle identity reduces the orbital degrees of freedom in two-particle systems and relates this to a phase factor depending on particle spin, clarifying the quantum nature of particle interchange.

Contribution

It establishes a direct connection between orbital degree reduction and the phase factor $(-1)^{2s}$ associated with particle interchange, highlighting a fundamental quantum symmetry.

Findings

Orbital degrees-of-freedom reduce from 6 to 5 due to particle identity.

The phase factor $(-1)^{2s}$ corresponds to particle interchange effects.

Redundancy in orbital motion description relates to particle spin and symmetry.

Abstract

It is shown that effects of particle identity entail reduction in the number of orbital degrees-of-freedom in non-relativistic 2-particle systems from 6 to 5. This effect of redundancy in description of orbital motion is found to be in correspondence to multiplicative phase factor $(-1)^{2s}$ which accompany interchange of the two particles, where $s$ is the spin of one particle.