De Sitter Space-time Symmetry Research Articles

One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry (II): — Higher Order Contributions

This is a follow of previous work entitled “One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry” [Commun. Theor. Phys. 57 (2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R2-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.

SUPERLUMINAL NEUTRINOS FROM SPECIAL RELATIVITY WITH DE SITTER SPACETIME SYMMETRY

We explore the recent OPERA experiment of superluminal neutrinos in the framework of special relativity with de Sitter spacetime symmetry (dS-SR). According to Einstein, a photon is treated as a massless particle in the framework of special relativity. In special relativity (SR) we have the universal parameter c, the photon velocity c photon and the phase velocity of a light wave in vacuum c wave = λν. Due to the null experiments of Michelson–Morley we have c = c wave . The parameter c photon is determined by the Noether charges corresponding to the spacetime symmetries of SR. In Einstein's special relativity (E-SR) we have c = c photon . In dS-SR, i.e. the special relativity with SO(4, 1) de Sitter spacetime symmetry, we have c photon > c. In this paper, the OPERA datum are examined in the framework of dS-SR. We show that OPERA anomaly is in agreement with the prediction of dS-SR with R≃1.95×1012 l.y. Based on the p-E relation of dS-SR, we also prove that the Cohen and Glashow's argument of possible superluminal neutrino's Cherenkov-like radiation is forbidden. We conclude that OPERA and ICARUS results are consistent and they are explained in the dS-SR framework.

ON DETERMINATION OF THE GEOMETRIC COSMOLOGICAL CONSTANT FROM THE OPERA EXPERIMENT OF SUPERLUMINAL NEUTRINOS

The recent OPERA experiment of superluminal neutrinos has deep consequences in cosmology. In cosmology a fundamental constant is the cosmological constant. From observations one can estimate the effective cosmological constant Λ eff which is the sum of the quantum zero point energy Λ dark energy and the geometric cosmological constant Λ. The OPERA experiment can be applied to determine the geometric cosmological constant Λ. It is the first study to distinguish the contributions of Λ and Λ dark energy from each other by experiment. The determination is based on an explanation of the OPERA experiment in the framework of Special Relativity with de Sitter spacetime symmetry.

Evidence for special relativity with de Sitter space-time symmetry

I show the formulation of de Sitter Special Relativity (dS-SR) based on Dirac-Lu-Zou-Guo's discussions. dS-SR quantum mechanics is formulated, and the dS-SR Dirac equation for hydrogen is suggested. The equation in the earth-QSO framework reference is solved by means of the adiabatic approach. It's found that the fine-structure “constant" α in dS-SR varies with time. By means of the t-z relation of the ΛCDM model, α's time-dependency becomes redshift z-dependent. The dS-SR's predictions of Δα/α agree with data of spectra of 143 quasar absorption systems, the dS-space-time symmetry is SO(3,2) (i.e., anti-dS group) and the universal parameter R (de Sitter ratio) in dS-SR is estimated to be R ≈ 2.73 × 1012 ly. The effects of dS-SR become visible at the cosmic space-time scale (i.e., the distance ≥ 109 ly). At that scale, dS-SR is more reliable than Einstein SR. The α-variation with time is evidence of SR with de Sitter symmetry.

Supersymmetries and their representations

We determine all manifest supersymmetries in more than 1 + 1 dimensions, including those with conformal or de Sitter space-time symmetry. For the supersymmetries in flat space we determine the structure of all representations and give formulae for an effective computation. In particular we show that at least for masses m 2 = 0, 1, 2 the states of the spinning string form supersymmetry multiplets.