Quantum poincaré group for isotropic quantum space-time

1994 ◽  
Vol 44 (11-12) ◽  
pp. 1101-1107
Author(s):  
Kordian Andrzej Smoliński
Keyword(s):  
Space Time ◽  
Quantum Space ◽  
Poincaré Group ◽  
Poincare Group

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals Mass in de Sitter and Anti-de Sitter Universes with Regard to Dark Matter

Universe ◽  
2020 ◽  
Vol 6 (5) ◽  
pp. 66 ◽  
Author(s):  
Jean-Pierre Gazeau
Keyword(s):  
Dark Matter ◽  
Irreducible Representation ◽  
Flat Space ◽  
Space Time ◽  
Energy Scale ◽  
Unitary Irreducible Representation ◽  
Poincaré Group ◽  
De Sitter ◽  
Rest Energy ◽  
Poincare Group

An explanation of the origin of dark matter is suggested in this work. The argument is based on symmetry considerations about the concept of mass. In Wigner’s view, the rest mass and the spin of a free elementary particle in flat space-time are the two invariants that characterize the associated unitary irreducible representation of the Poincaré group. The Poincaré group has two and only two deformations with maximal symmetry. They describe respectively the de Sitter (dS) and anti-de Sitter (AdS) kinematic symmetries. Analogously to their shared flat space-time limit, two invariants, spin and energy scale for de Sitter and rest energy for anti-de Sitter, characterize the unitary irreducible representation associated with dS and AdS elementary systems, respectively. While the dS energy scale is a simple deformation of the Poincaré rest energy and so has a purely mass nature, AdS rest energy is the sum of a purely mass component and a kind of zero-point energy derived from the curvature. An analysis based on recent estimates on the chemical freeze-out temperature marking in Early Universe the phase transition quark–gluon plasma epoch to the hadron epoch supports the guess that dark matter energy might originate from an effective AdS curvature energy.

Coupling between the Poincaré Group and Space-Time or Spacelike Reflections on Hyperplanes

1968 ◽  
Vol 174 (5) ◽  
pp. 1625-1630 ◽  
Author(s):  
James T. Miller ◽  
Gordon N. Fleming
Keyword(s):  
Space Time ◽  
Poincaré Group ◽  
Poincare Group

scholarly journals On the structure and applications of the Bondi–Metzner–Sachs group

2018 ◽  
Vol 15 (02) ◽  
pp. 1830002 ◽  
Author(s):  
Francesco Alessio ◽  
Giampiero Esposito
Keyword(s):  
Minkowski Space ◽  
Isometry Group ◽  
Black Hole Physics ◽  
Flat Space ◽  
Space Time ◽  
Poincaré Group ◽  
Poincare Group ◽  
Curved Space ◽  
Asymptotically Flat ◽  
Minkowski Space Time

This work is a pedagogical review dedicated to a modern description of the Bondi–Metzner–Sachs (BMS) group. Minkowski space-time has an interesting and useful group of isometries, but, for a generic space-time, the isometry group is simply the identity and hence provides no significant informations. Yet symmetry groups have important role to play in physics; in particular, the Poincaré group describing the isometries of Minkowski space-time plays a role in the standard definitions of energy-momentum and angular-momentum. For this reason alone it would seem to be important to look for a generalization of the concept of isometry group that can apply in a useful way to suitable curved space-times. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work, the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of “asymptotic simplicity” are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the BMS group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the BMS group, e.g. its algebra and the possibility to obtain as its subgroup the Poincaré group, as we may expect. The paper ends with a review of the BMS invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.

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