Anyon spin and the exotic central extension of the planar Galilei group

TL;DR

This paper demonstrates that in (2+1) dimensions, the second central extension of the Galilei group is associated with any real-valued spin, revealing an exotic extension in planar physics.

Contribution

It establishes a direct link between the second central extension of the Galilei group and any real spin value, highlighting an exotic extension in planar Galilean symmetry.

Findings

Second central extension corresponds to any real spin

Reveals an exotic extension of the planar Galilei group

Connects group theory with physical spin in 2+1 dimensions

Abstract

We show that the second central extension of the Galilei group in (2+1) dimensions corresponds to spin, which can be any real number.