Realizations of the Unitary Representations of the Inhomogeneous Space-Time Groups II. Covariant Realizations of the Poincaré Group

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

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

International Journal of Modern Physics A ◽

10.1142/s0217751x10051050 ◽

2010 ◽

Vol 25 (31) ◽

pp. 5765-5785 ◽

Cited By ~ 12

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.

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

Universe ◽

10.3390/universe6050066 ◽

2020 ◽

Vol 6 (5) ◽

pp. 66 ◽

Cited By ~ 1

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.

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