Unitary representations of the (4+1) de Sitter group on unitary irreducible representation spaces of the Poincaré group: Equivalence with their realizations as induced representations

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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IS PHYSICS ASKING FOR A NEW KINEMATICS?

International Journal of Modern Physics D ◽

10.1142/s0218271808013972 ◽

2008 ◽

Vol 17 (13n14) ◽

pp. 2485-2493 ◽

Cited By ~ 4

Author(s):

R. ALDROVANDI ◽

J. G. PEREIRA

Keyword(s):

Special Relativity ◽

Planck Scale ◽

Poincaré Group ◽

De Sitter ◽

Sitter Group ◽

Poincare Group

It is discussed whether some of the consistency problems of present day physics could be solved by replacing special relativity, whose underlying kinematics is ruled by the Poincaré group, with de Sitter relativity, whose underlying kinematics is ruled by the de Sitter group. In contrast to ordinary special relativity, which seems to fail at the Planck scale, this new relativity is "universal," in the sense that it holds at all energy scales.

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The localizability of particles in de Sitter space

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100049896 ◽

1971 ◽

Vol 70 (2) ◽

pp. 283-302 ◽

Cited By ~ 21

Author(s):

K. C. Hannabuss

Keyword(s):

De Sitter Space ◽

Geometrical Interpretation ◽

Iwasawa Decomposition ◽

Poincaré Group ◽

De Sitter ◽

Negative Mass ◽

Sitter Group ◽

Poincare Group

AbstractMotivated by the Iwasawa decomposition and its geometrical interpretation, two new decompositions of the de Sitter group are obtained. The first is applied to construct the representations of the de Sitter group in a form immediately comparable with those of the Poincaré group. In particular they act on functions over an hyperboloid like the momentum hyperboloid of the Poincaré group, although they require both positive and negative mass shells of that hyperboloid. Using the second decomposition it is shown that the representations of the de Sitter group are localizable in the sense of Mackey and Wightman. Position operators are exhibited.

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