Fermions with spin 1/2 as global SO(3) vortices

TL;DR

This paper demonstrates that the nontrivial topology of the SO(3) rotation group in four-dimensional Euclidean space necessitates the existence of fermions as global vortices, contrasting with bosons which are topologically trivial.

Contribution

It establishes a topological origin for fermions as vortices in the SO(3) group space, linking spin structures to fundamental particle properties.

Findings

Fermions correspond to nontrivial elements of π₁(SO(3))

Bosons are topologically trivial in SO(3)

Spin structures imply fermionic vortices in 4D Euclidean space

Abstract

In this paper we show that the nontrivial fundamental group $\pi_1 SO(3) ={\Bbb Z}_2$ for the group SO(3) of global proper rotations of a four-dimensional Euclidian space (when a spin structure is introduced preliminarily in that space) implies always fermions as global SO(3) vortices, while bosons can be reduced to trivial lines (contracted into a point) in the SO(3) group space.