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 Irreducibility of some unitary representations of the poincaré group with respect to the Poincaré subsemigroup, II

1982 ◽  
Vol 87 ◽  
pp. 147-174 ◽  
Author(s):  
Hitoshi Kaneta
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Unitary Representations ◽  
Poincaré Group ◽  
Poincare Group ◽  
3 Dimensional ◽  
The Matrix ◽  
Dimensional Space Time

Let P+(3) and P+(3) be the 3-dimensional space-time Poincaré group and the Poincaré subsemigroup, that is, P(3) = R3 × sSU(1, 1) and P+(3) = V+(3)=SSU(1, 1) where The multiplication is defined by the formula (x, g)(x′, g′) = (x + g*−1x′g−1, gg′) for x, x′ ∈ R3 and g, g′ ∈ SU(l, 1). Here x = (x0, x1, x2) is identified with the matrix

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.

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 Chern-Simons-Antoniadis-Savvidy Forms and Non-Abelian Anomaly

2019 ◽  
Vol 8 (1) ◽  
pp. 11-15
Author(s):  
Suhaivi Hamdan ◽  
Erwin Erwin ◽  
Saktioto Saktioto
Keyword(s):  
Field Strength ◽  
Gauge Transformation ◽  
Integral Form ◽  
Gauge Fields ◽  
Gauge Invariant ◽  
Time Coordinate ◽  
Form Analysis ◽  
Yang Mills ◽  
Chern Simons ◽  
Gauge Variation

Kuat medan tensor yang ditransformasikan secara homogen terhadap perluasan transformasi gauge memenuhi bentuk sifat invarian gauge. Analisa invarian gauge dalam bantuk integeralnya memperlihatkan hubungan dengan koordinat ruang-waktu yang menunjukan bentuk baru dari topologi Lagrangian. Sifat invarian dari bentuk Pontryagin-Chern terhadap kuat medan tensor non-Abelian dan lemma Poincare dapat digunakan untuk mengkontruksi bentuk ChSAS yang menunjukan sifat quasi-invarian dibawah transformasi gauge. Artikel ini bertujuan untuk membuktikan bahwa kuat medan tensor Yang-Mills dari bentuk ChSAS memilik variasi gauge anomali non-Abelian seperti pada bentuk Chern-Simons. Integrasi bentuk ChSAS menghasilkan dimensi-4, 6 dan 8 variasi gauge genap dan memperlihatkan hubungan dengan bentuk Chern-Simons dimensi-3 dan 5 untuk variasi gauge ganjil. Bentuk ChSAS memperlihatkan variabel lebih kompleks yang menujukan sifat berosilasi. Tensors field strength transformation homogeneously to extend gauge transformation fulfilling charateristic gauge invariant form. Analysis gauge invariant in integral form shows corresponding with space-time coordinate that prove new topology Lagrangians form. Furthermore invariant charateristic of Pontryagin-Chern to non-Abelian tensor gauge fields and lemma Poincare used to contruct ChSAS forms which shows quasi-inavriant under gauge transformation. This paper aims to prove Yang-Mills tensor gauge field of ChSAS forms has variation non-Abelian anomaly like Chern-Simons forms. The integration ChSAS forms resulted 4, 6 and 8-dimensional even gauge variation which also correspond 3 and 5-dimensional odd gauge variation Chern-Simons forms. The ChSAS forms also showed complex variable and osilation.  Keywords: Pontryagin-Chern, Kuat medan tensor non-Abelian, Chern-Simans-Antoniadis-Savvidy, Anomali Non-Abelian.

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