Super algebra and Harmonic Oscillator in Anti de Sitter space

‎Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter‎ ‎space or anti-de Sitter space

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

Cohomogeneity One Anti De Sitter Space H_1^3

The clash between de Sitter and anti-de Sitter space

We investigate solutions that are dynamically evolving between asymptotically de Sitter and asymptotically anti-de Sitter regions in the context of Einstein gravity coupled to general matter fields in d dimensions. We demonstrate the existence of a no go theorem whenever the matter content of the theory is ‘reasonable’, i.e., such that the weak energy condition is satisfied. We show that there ...

Quantum Anti-de Sitter Space

The quantum Anti-de Sitter (AdS) group and quantum AdS space is discussed. Ways of getting the quantum AdS group from real forms of quantum orthogonal group are presented. Differential calculus on the quantum AdS space are also introduced. In particular, reality of differential calculus are given. We set up explicit relationships between quantum group and quantum algebra, which can be refereed ...

FREE EQUATIONS FOR MASSIVE MATTER FIELDS IN 2+1 -DIMENSIONAL ANTI-DE SITTER SPACE From DEFORMED OSCILLATOR ALGEBRA

We reformulate free equations of motion for massive spin 0 and spin 1/2 matter fields in 2+1 dimensional anti-de Sitter space in the form of some covariant constantness conditions. The infinite-dimensional representation of the anti-de Sitter algebra underlying this formulation is shown to admit a natural realization in terms of the algebra of deformed oscillators with a deformation parameter r...

Brane Collisions in Anti-de Sitter Space

From the requirement of continuous matching of bulk metric around the point of brane collision we derive a conservation law for collisions of p-branes in (p+2)-dimensional space-time. This conservation law relates energy densities on the branes before and after the collision. Using this conservation law we are able to calculate the amount of matter produced in the collision of orbifoldfixed bra...