A Geometric Proof of the Spin-Statistics Theorem From Cubic Lattice Rotation Symmetry to the Fermion Exchange Sign

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.