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

24th International Conference on Integrable Systems and Quantum symmetries

Melas, Evangelos^1

University of Athens, Department of Economics, Unit of Mathematics and Informatics, Sofokleous 1, Athens

10559, Greece^1

关键词: Asymptotic symmetry;    Cyclic group;    Even orders;    General Relativity;    Invariant systems;    Locally compact;    Symmetry groups;    Unitary representations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/804/1/012030/pdf
DOI  :  10.1088/1742-6596/804/1/012030

来源: IOP

【 摘 要 】

The original Bondi-Metzner-Sachs group B is the common asymptotic symmetry group of all asymptotically at 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 construct the IRS of B(2, 1), the analogue of B, in 3 space-time dimensions. 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.