Unique distinction of the Lorentz and the anti-de Sitter group in the classical Kepler problem

1977 ◽  
Vol 16 (6) ◽  
pp. 409-417 ◽  
Author(s):  
J. Stickforth
Keyword(s):  
Kepler Problem ◽  
De Sitter ◽  
Sitter Group

De Sitter symplectic spaces and their quantizations

1974 ◽  
Vol 76 (2) ◽  
pp. 473-480 ◽  
Author(s):  
J. H. Rawnsley
Keyword(s):  
Lorentz Group ◽  
Bound States ◽  
Kepler Problem ◽  
Classical System ◽  
De Sitter ◽  
Sitter Group ◽  
Group Spin ◽  
Theoretical View ◽  
Simply Connected ◽  
Inhomogeneous Lorentz Group

The de Sitter group, Spin (4, 1), is a simply connected, semi-simple, ten-dimensional Lie group which can be contracted to the inhomogeneous Lorentz group. Physical systems with the de Sitter group as asymmetry group should resemble those of the inhomogeneous Lorentz group and may provide an alternative to these systems of special-relativistic physics. Details of physics in de Sitter space from the group theoretical view-point are given in (3). The de Sitter group is also known to be a symmetry group for the bound states of the hydrogen atom, and recent work has shown how this group acts on the corresponding classical system, the Kepler problem. See (8).

scholarly journals Effect of GUP on the Kepler problem and a variable minimal length

2014 ◽  
Vol 92 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Fatemeh Ahmadi ◽  
Jafar Khodagholizadeh
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Kepler Problem ◽  
Rotational Symmetry ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Minimal Length ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Perihelion Shift

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg uncertainty principle near the Plank scale, known as the generalized uncertainty principle (GUP). Here we study the effects of GUP, which preserves the rotational symmetry of the space–time, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild – de Sitter space–time with the resultant value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the space–time. Now, if the cosmological constant varies with time, we have a variable minimal length in the space–time. Finally, we investigate the effects of GUP on the stability of circular orbits.

scholarly journals A CHERN–SIMONS E8 GAUGE THEORY OF GRAVITY IN D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES

2007 ◽  
Vol 04 (08) ◽  
pp. 1239-1257 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Gauge Theory ◽  
Grand Unification ◽  
De Sitter ◽  
Sitter Group ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
M Theory ◽  
Chern Simons ◽  
Topological Part ◽  
Gauge Theory Of Gravity

A novel Chern–Simons E8 gauge theory of gravity in D = 15 based on an octicE8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern–Simons E8 gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E8 Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E8 gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E8 gauge theory remains unknown. We hope that the Chern–Simons E8 gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

scholarly journals Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

scholarly journals THE STRUCTURE OF ADS BLACK HOLES AND CHERN–SIMONS THEORY IN 2 + 1 DIMENSIONS

1999 ◽  
Vol 14 (04) ◽  
pp. 505-520 ◽  
Author(s):  
SHARMANTHIE FERNANDO ◽  
FREYDOON MANSOURI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gauge Theory ◽  
Excited States ◽  
Simons Theory ◽  
De Sitter ◽  
Sitter Group ◽  
Ads Black Holes ◽  
Chern Simons ◽  
Chern Simons Theory

We study anti-de Sitter black holes in 2 + 1 dimensions in terms of Chern–Simons gauge theory of the anti-de Sitter group coupled to a source. Taking the source to be an anti-de Sitter state specified by its Casimir invariants, we show how all the relevant features of the black hole are accounted for. The requirement that the source be a unitary representation leads to a discrete tower of excited states which provide a microscopic model for the black hole.

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