On the representation theory of the Bondi–Metzner–Sachs group and its variants in three space–time dimensions

@article{Melas2017OnTR,
  title={On the representation theory of the Bondi–Metzner–Sachs group and its variants in three space–time dimensions},
  author={Evangelos Melas},
  journal={Journal of Mathematical Physics},
  year={2017},
  volume={58},
  pages={071705}
}
  • E. Melas
  • Published 17 March 2017
  • Mathematics
  • Journal of Mathematical Physics
The original Bondi–Metzner–Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian radiating 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, 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 the BMS group B in 3 space–time… 
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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
Lie theory for asymptotic symmetries in general relativity: The BMS group
We study the Lie group structure of asymptotic symmetry groups in general relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic
From parabolic to loxodromic BMS transformations
Half of the Bondi–Metzner–Sachs (BMS) transformations consist of orientation-preserving conformal homeomorphisms of the extended complex plane known as fractional linear (or Möbius) transformations.
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This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention:
The Asymptotic Structure of Gravity in Higher Even Dimensions
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A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009
(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p
From parabolic to loxodromic gravity
Half of the Bondi-Metzner-Sachs (BMS) transformations consist of orientation-preserving conformal homeomorphisms of the extended complex plane known as fractional linear (or Mobius) transformations.

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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
On irreducible representations of the ultrahyperbolic BMS group
Lifting of projective representations of the Bondi—Metzner—Sachs group
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Following some motivating remarks on the role of group theory in physics, it is explained how a systematic study of the asymptotic symmetry group of general relativity, the Bondi-Metzner-Sachs group,
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The ordinary Bondi–Metzner–Sachs (BMS) group B is the common asymptotic symmetry group of all radiating, asymptotically flat, Lorentzian spacetimes. As such, B is the best candidate for the universal
Representations of the ultrahyperbolic BMS group HB.II. Determination of the representations induced from infinite little groups
The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space-times. As such, B is the best candidate for the universal symmetry
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    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1972
Following a historical introduction, it is suggested that irreducible unitary representations of the Bondi-Metzner-Sachs group may be used to classify elementary particles in a quantum theory which
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The ordinary Bondi–Metzner–Sachs (BMS) group B is the best candidate for the fundamental symmetry group of General Relativity. It has been shown that B admits generalizations to real space–times of
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The Bondi-Metzner-Sachs group B is the common asymptotic group of all asymptotically flat (lorentzian) space-times, and is the best candidate for the universal symmetry group of general relativity.
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    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
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The Bondi-Metzner-Sachs group is topologized as a nuclear Lie group, and it is shown th at irreducible representations arise from either (i) transitive SL{2,C) actions on supermomentum space, or (ii)
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A bstractThe Bondi-Metzner-Sachs group in three dimensions is the symmetry group of asymptotically flat three-dimensional spacetimes. It is the semi-direct product of the diffeomorphism group of the
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