The de Sitter relativistic top theory

Armenta, Joel Angulo; Nieto, J. A.

doi:10.1063/1.1827923

Cited by 8 publications

(8 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The unit vector in the radial direction has for componentsr = ( r/r) = (x 1 /r, x 2 /r, x 3 /r). It is warranted to study the full relativistic dynamics as well, in particular the modif ied relativistic dynamics of the de-Sitter rigid top [41] due to the effects of Yang's Noncommutative spacetime algebra . The de Sitter rigid Top can be generalized further to Clifford spaces since a Clifford-polyparticle has more degrees of freedom than a relativistic top in ordinary spacetimes [40] .…”

Section: On the Noncommutative Yang's Spacetime Algebra Holography Amentioning

confidence: 99%

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

Castro

2005

Found Phys

View full text Add to dashboard Cite

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper and lower length scales (infrared/ultraviolet cutoff ). The invariance symmetry leads naturally to the real Clifford algebra Cl(2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. We proceed with an extensive review of Smith's 8D model based on the Clifford algebra Cl(1, 7) that reproduces at low energies the physics of the Standard Model and Gravity; including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Further results by Smith are discussed pertaining the interplay among Clifford, Jordan, Division and Exceptional Lie algebras within the hierarchy of dimensions D = 26, 27, 28 related to bosonic string, M, F theory. Two Geometric actions are presented like the Clifford-Space extension of Maxwell's Electrodynamics, Brandt's action related the 8D spacetime tangent-bundle involving coordinates and velocities ( Finsler geometries ) followed by a discussion ( based on results by Cho et al ) why Einstein's gravity in m + n dimensions is equivalent to an m-dim Yang-Mills-like theory of diffemorphisms of an internal n-dim space which admits a holographic reduction to lower dimensions in the case of AdS m ×S n and dS m ×H n backgrounds. Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit.

show abstract

Section: On the Noncommutative Yang's Spacetime Algebra Holography Amentioning

confidence: 99%

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

Castro

2005

Found Phys

View full text Add to dashboard Cite

show abstract

“…The variable m is the conjugate to the Stuckelberg evolution parameter s that allowed Pavsic to propose a natural solution of the problem of time in Quantum Cosmology [3] . Eq-(2-12c) is a generalization (more degrees of freedom) of the de Sitter top studied in [48]. Nottale has given convincing arguments why the notion of dimension is resolution dependent, and at the Planck scale, the minimum attainable distance, the dimension becomes singular, that is blows-up.…”

Section: The Generalized String/brane Uncertainty Relationsmentioning

confidence: 99%

On modified Weyl–Heisenberg algebras, noncommutativity, matrix-valued Planck constant and QM in Clifford spaces

Castro¹

2006

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

A novel Weyl-Heisenberg algebra in Clifford-spaces is constructed that is based on a matrix-valued H AB extension of Planck's constant. As a result of this modified Weyl-Heisenberg algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, p x); (x, p y); (x, p z); (y, p x), ... with absolute precision. New Klein-Gordon and Dirac wave equations and dispersion relations in Clifford-spaces are presented. The latter Dirac equation is a generalization of the Dirac-Lanczos-Barut-Hestenes equation. We display the explicit isomorphism between Yang's Noncommutative space-time algebra and the area-coordinates algebra associated with Clifford spaces. The former Yang's algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p =h/R (maximal length R, infrared cutoff). The double-scaling limit of Yang's algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L 2 = nλ 2 (in Planck area units) given in terms of the discrete angular-momentum eigenvalues n. It is shown how Modified Newtonian dynamics is also a consequence of Yang's algebra resulting from the modified Poisson brackets. Finally, another noncommutative algebra (which differs from the Yang's algebra) and related to the minimal length uncertainty relations is presented. We conclude with a discussion of the implications of Noncommutative QM and QFT's in Clifford-spaces.

show abstract

“…Equilibrium conditions for spinning particles in a Kerr-de Sitter space-time was considered in [18]. A relativistic top theory has been discussed in [19] from the point of view of the de Sitter group and some other mathematical aspects of this theory has been studied in [20].…”

Section: Introductionmentioning

confidence: 99%

Spinning particles in Schwarzschild–de Sitter space–time

Mortazavimanesh

Mohseni

2009

Gen Relativ Gravit

View full text Add to dashboard Cite

After considering the reference case of the motion of spinning test bodies in the equatorial plane of the Schwarzschild space-time, we generalize the results to the case of the motion of a spinning particle in the equatorial plane of the Schwarzschild-de Sitter space-time. Specifically, we obtain the loci of turning points of the particle in this plane. We show that the cosmological constant affect the particle motion when the particle distance from the black hole is of the order of the inverse square root of the cosmological constant.

show abstract

The de Sitter relativistic top theory

Cited by 8 publications

References 24 publications

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

On modified Weyl–Heisenberg algebras, noncommutativity, matrix-valued Planck constant and QM in Clifford spaces

Spinning particles in Schwarzschild–de Sitter space–time

Contact Info

Product

Resources

About