scholarly journals Coadjoint Orbits of the Poincaré Group for Discrete-Spin Particles in Any Dimension

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1749
Author(s):  
Ismael Ahlouche Lahlali ◽  
Nicolas Boulanger ◽  
Andrea Campoleoni
Keyword(s):  
Coadjoint Orbits ◽  
Poincaré Group ◽  
Continuous Spin ◽  
Massless Particles ◽  
Poincare Group

Considering the Poincaré group ISO(d−1,1) in any dimension d>3, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how our analysis extends to the case of continuous spin.

scholarly journals Gravitational edge modes, coadjoint orbits, and hydrodynamics

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
William Donnelly ◽  
Laurent Freidel ◽  
Seyed Faroogh Moosavian ◽  
Antony J. Speranza
Keyword(s):  
General Relativity ◽  
Boundary Surface ◽  
Infinite Family ◽  
Symmetry Algebra ◽  
Complete Classification ◽  
Coadjoint Orbits ◽  
Poincaré Group ◽  
Poincare Group ◽  
Dimensional Group

Abstract The phase space of general relativity in a finite subregion is characterized by edge modes localized at the codimension-2 boundary, transforming under an infinite-dimensional group of symmetries. The quantization of this symmetry algebra is conjectured to be an important aspect of quantum gravity. As a step towards quantization, we derive a complete classification of the positive-area coadjoint orbits of this group for boundaries that are topologically a 2-sphere. This classification parallels Wigner’s famous classification of representations of the Poincaré group since both groups have the structure of a semidirect product. We find that the total area is a Casimir of the algebra, analogous to mass in the Poincaré group. A further infinite family of Casimirs can be constructed from the curvature of the normal bundle of the boundary surface. These arise as invariants of the little group, which is the group of area-preserving diffeomorphisms, and are the analogues of spin. Additionally, we show that the symmetry group of hydrodynamics appears as a reduction of the corner symmetries of general relativity. Coadjoint orbits of both groups are classified by the same set of invariants, and, in the case of the hydrodynamical group, the invariants are interpreted as the generalized enstrophies of the fluid.

scholarly journals Adjoint and Coadjoint Orbits of the Poincaré Group

2006 ◽  
Vol 90 (1-2) ◽  
pp. 65-89 ◽  
Author(s):  
Richard Cushman ◽  
Wilberd van der Kallen
Keyword(s):  
Coadjoint Orbits ◽  
Poincaré Group ◽  
Poincare Group

scholarly journals Massless finite and infinite spin representations of Poincaré group in six dimensions

2021 ◽  
pp. 136064
Author(s):  
I.L. Buchbinder ◽  
S.A. Fedoruk ◽  
A.P. Isaev ◽  
M.A. Podoinitsyn
Keyword(s):  
Poincaré Group ◽  
Poincare Group ◽  
Six Dimensions ◽  
Spin Representations

scholarly journals Completing Multiparticle Representations of the Poincaré Group

2021 ◽  
Vol 127 (4) ◽  
Author(s):  
Csaba Csáki ◽  
Sungwoo Hong ◽  
Yuri Shirman ◽  
Ofri Telem ◽  
John Terning
Keyword(s):  
Poincaré Group ◽  
Poincare Group

TWISTED POINCARE GROUP AND SPIN-STATISTICS

2005 ◽  
Vol 20 (27) ◽  
pp. 6268-6277 ◽  
Author(s):  
ALEKSANDR PINZUL
Keyword(s):  
Field Theory ◽  
Tensor Product ◽  
Poincaré Group ◽  
Commutative Field ◽  
Poincare Group ◽  
Quantized Fields

Recently it has been shown that it is possible to retain the Lorentz-invariant interpretation of the non-commutative field theory.1,2,3 This was achieved by the means of the twisted action of the Poincaré group on the tensor product of the fields. We investigate the consequences of this approach for the quantized fields.

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