Abstract: This work provides a geometric proof that the exchange of two identical spin-1/2 particles necessarily produces a minus sign. The proof relies only on the SU (2) double cover of the spatial rotation group: the identity S (−n, π) = −S (n, π), which follows directly from S (2π) = −I, yields the factor (−1) ^ (2s) = −1 for s=1/2. The exchange operation is modeled as a continuous adiabatic process in which each particle rotates by π about the midpoint of their separation. No assumptions about anticommutation relations or quantum field theory are required.
卓冰 蒋 (Sun,) studied this question.