scholarly journals The bicovariant differential calculus on the κ-Poincaré group and on the κ-Minkowski space

1996 ◽  
Vol 46 (2-3) ◽  
pp. 201-208 ◽  
Author(s):  
Piotr Kosiński ◽  
Paweł Maślanka ◽  
Jan Sobczyk
Keyword(s):  
Minkowski Space ◽  
Differential Calculus ◽  
Poincaré Group ◽  
Poincare Group ◽  
Bicovariant Differential Calculus

scholarly journals Bicovariant differential calculus on the quantum D=2 Poincaré group

1992 ◽  
Vol 279 (3-4) ◽  
pp. 291-298 ◽  
Author(s):  
Leonardo Castellani
Keyword(s):  
Differential Calculus ◽  
Poincaré Group ◽  
Poincare Group ◽  
Bicovariant Differential Calculus

scholarly journals BICOVARIANT CALCULUS ON TWISTED ISO(N), QUANTUM POINCARÉ GROUP AND QUANTUM MINKOWSKI SPACE

1996 ◽  
Vol 11 (25) ◽  
pp. 4513-4549 ◽  
Author(s):  
PAOLO ASCHIERI ◽  
LEONARDO CASTELLANI
Keyword(s):  
Minkowski Space ◽  
Classical Limit ◽  
Poincaré Group ◽  
Poincare Group

A bicovariant calculus on the twisted inhomogeneous multiparametric q groups of the Bn, Cn, Dn types, and on the corresponding quantum planes, is found by means of a projection from the bicovariant calculus on Bn+1, Cn+1, Dn+1. In particular we obtain the bicovariant calculus on a dilatation-free q Poincaré group ISO q(3, 1), and on the corresponding quantum Minkowski space. The classical limit of the Bn, Cn, Dn bicovariant calculus is discussed in detail.

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.

scholarly journals The isotropy mappings of Minkowski space-time generate the orthochronous poincaré group

1990 ◽  
Vol 31 (4) ◽  
pp. 425-433
Author(s):  
John W. Schutz
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Coordinate Frame ◽  
Poincaré Group ◽  
Position Space ◽  
Poincare Group ◽  
Coordinate Frames ◽  
Minkowski Space Time ◽  
Lorentz Boosts ◽  
Single Coordinate

AbstractMinkowski space-time is specified with respect to a single coordinate frame by the set of timelike lines. Isotropy mappings are defined as automorphisms which leave the events of one timelike line invariant. We demonstrate the existence of two special types of isotropy mappings. The first type of isotropy mapping induce orthogonal transformations in position space. Mappings of the second type can be composed to generate Lorentz boosts. It is shown that isotropy mappings generate the orthochronous Poincaré group of motions. The set of isotropy mappings then maps the single assumed coordinate frame onto a set of coordinate frames related by transformations of the orthochronous Poincaré group.

ISOTROPIC QUANTIZED MINKOWSKI SPACE AND POINCARÉ GROUP

2002 ◽  
Author(s):  
KORDIAN ANDRZEJ SMOLIŃSKI
Keyword(s):  
Minkowski Space ◽  
Poincaré Group ◽  
Poincare Group

scholarly journals On Poisson structures related to κ-Poincaré Group

2017 ◽  
Vol 14 (09) ◽  
pp. 1750133 ◽  
Author(s):  
Piotr Stachura
Keyword(s):  
Minkowski Space ◽  
Poisson Structure ◽  
Lie Algebroid ◽  
Poisson Structures ◽  
Poincaré Group ◽  
Poincare Group ◽  
Affine Minkowski Space

The Poisson structure related to [Formula: see text]-Poincaré Group is explicitly presented as a dual to a certain Lie algebroid in a geometric and coordinate-free way. The related Poisson structure on the (affine) Minkowski space is also presented in a geometric way.

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