The Projective Unitary Irreducible Representations of the Poincar\'e Group in 1+2 Dimensions

TL;DR

This paper classifies all projective unitary irreducible representations of the Poincaré group in 1+2 dimensions, using Mackey's theorem and explicit formulas for the universal cover of the Lorentz group.

Contribution

It provides a complete and explicit characterization of these representations, which was not previously available.

Findings

Explicit formulas for all representations are derived.

Complete classification of projective unitary irreducible representations in 1+2 dimensions.

Application of Mackey's theorem to this classification.

Abstract

We give a complete analysis of the projective unitary irreducible representations of the Poincar\'e group in 1+2 dimensions applying Mackey theorem and using an explicit formula for the universal covering group of the Lorentz group in 1+2 dimensions. We provide explicit formulae for all representations.