Coadjoint Orbits of the Poincar\'e Group in 2+1 Dimensions and their Coherent States

TL;DR

This paper analyzes the coadjoint orbits of the 2+1 Poincaré group, linking them to irreducible representations and constructing coherent states for specific orbit types.

Contribution

It provides a detailed study of the orbit structure, connects orbits to irreducible representations, and constructs coherent states for hyperboloidal and conical orbits.

Findings

Classification of coadjoint orbits for the 2+1 Poincaré group

Explicit construction of coherent states for certain orbits

Connection between orbits and irreducible group representations

Abstract

We study the structure of the coadjoint orbits of the 2+1 Poincar\'e group, using a matricial representation of the group. We also obtain the orbits connected to irreducible representations of the group. Finally we obtain coherent states for the hyperboloidal and conical orbits.