Representations of the ultrahyperbolic BMS group UHB(2, 2). I. General Results

[摘要] The ordinary Bondi - Metzner - Sachs (BMS) group B is the common asymptotic symmetry group of all radiating, asymptotically flat, Lorentzian space - times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). However, in studying quantum gravity, space - times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. In particular, the generalisation B(2, 2) appropriate to the ultrahyperbolic signature (+,+, - , - ) has been described in detail, and the study of its irreducible unitary representations (IRs) of B(2, 2) has been initiated. We continue this programme by introducing a new group UHB(2, 2) in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of B(2, 2). In this paper we report on the first general results on the representation theory of UHB(2, 2). In particular the main general results are that the all little groups of UHB(2, 2) are compact and that the Wigner - Mackey's inducing construction is exhaustive despite the fact that UHB(2, 2) is not locally compact in the employed Hilbert topology.

[发布机构] Technological Educational Institution of Lamia, Department of Informatics, 3nd National Road, Athens - Lamia; 35100, Greece^1

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Asymptotic symmetry;General Relativity;Locally compact;Lorentzian space;Representation theory;Symmetry groups;Theoretical study;Unitary representations