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

Abstract

In this paper we show that the nontrivial fundamental group ${\pi }_{1}SO(3)={\mathbb{Z}}_2$ 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.

26 pages, 7 eps.figures, LaTeX