The Projective Unitary Irreducible Representations of the Galilei Group in 1+2 Dimensions

TL;DR

This paper classifies all projective unitary irreducible representations of the Galilei group in 1+2 dimensions by analyzing its multiplicator group, providing a foundational understanding of its representation theory.

Contribution

It offers a complete list of projective unitary irreducible representations of the Galilei group in 1+2 dimensions for non-trivial multiplicators, based on elementary analysis.

Findings

List of all projective unitary irreducible representations identified

Analysis of the multiplicator group of the Galilei group in 1+2 dimensions

Provides a foundational framework for understanding Galilei group representations

Abstract

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of $G^{\uparrow}_{+}$.