• DOI:10.1088/1742-6596/804/1/012030
• Corpus ID: 126113281

Representations of the Bondi—Metzner—Sachs group in three space—time dimensions

@inproceedings{Melas2017RepresentationsOT,
  title={Representations of the Bondi—Metzner—Sachs group in three space—time dimensions},
  author={Evangelos Melas},
  year={2017}
}

• E. Melas
• Published 1 August 2021
• Mathematics

The original Bondi−Metzner−Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian 4−dim space−times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). In 1973, with this motivation, P. J. McCarthy classified all relativistic B−invariant systems in terms of strongly continuous irreducible unitary representations (IRS) of B. Here, we introduce the analogue B(2, 1) of Bondi−Metzner−Sachs group in 3 space−time dimensions. We obtain the necessary data in order to construct the IRS of B(2, 1). The main results of the representation theory are: The IRS are induced from “little groups” which are compact. The finite “little groups” are cyclic groups of even order. The inducing construction is exhaustive notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.