Related papers: From the Complete Yang Model to Snyder's Model, de…
We show that if Yang's model as the earliest TSR is completed, it should contain both Snyder's quantized space-time model as the earliest DSR, the de Sitter SR and their duality.
We consider generalizations of the Snyder algebra to a curved spacetime background with de Sitter symmetry. As special cases, we obtain the algebras of the Yang model and of triply special relativity. We discuss the realizations of these…
Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum…
We consider an Einstein-Yang-Mills Lagrangian in a five dimensional space-time including a cosmological constant. Assuming all fields to be independent of the extra coordinate, a dimensional reduction leads to an effective (3+1)-dimensional…
There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the \dS-invariant special relativity. This indicates that physics at the Planck length $\ell_P$ and the scale $R=3/\Lambda$ should be dual to each…
In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate…
Three dimensional Dirac oscillator was considered in deformed space obeyed to deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations gives rise to appearance minimal uncertainty in position…
Long time ago, C.N. Yang proposed a model of noncommutative spacetime that generalized the Snyder model to a curved background. In this paper we review his proposal and the generalizations that have been suggested during the years. In…
We show that Doubly Special Relativity (DSR) can be viewed as a theory with energy-momentum space being the four dimensional de Sitter space. Different formulations (bases) of the DSR theory considered so far can be therefore understood as…
The relativistic Lorentz-covariant quantum space-times obtained by Snyder can be described by the coset generators of (anti) de-Sitter algebras. Similarly, the Lorentz-covariant quantum phase spaces introduced by Yang, which contain…
We present the basic $\mathcal{N} =1$ superconformal field theories in four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills theory and the chiral multiplet theory with gauge interactions or cubic superpotential.…
We discuss the generalization of Doubly Special Relativity to a curved de Sitter background. The model has three observer-independent scales, the velocity of light $c$, the radius of curvature of the geometry $\alpha$, and the Planck energy…
A surprising connection exists between double-scaled SYK at infinite temperature, and large N QCD. The large N expansions of the two theories have the same form; the 't Hooft limit of QCD parallels the fixed p limit of SYK (for a theory…
We study the deformed conformal-Poincare symmetries consistent with the Snyder--de Sitter space. A relativistic particle model invariant under these deformed symmetries is given. This model is used to provide a gauge independent derivation…
The relativistic $D=4$ Snyder model is formulated in terms of $D=4$ $dS$ algebra $o(4,1)$ generators, with noncommutative Lorentz-invariant Snyder quantum space-time provided by $\frac{O(4,1)}{O(3,1)}$ coset generators. Analogously, in…
The discrete symmetries of the Dirac field on the de Sitter manifold are studied taking into account that this has two portions that can play the role of physical space-times, namely the expanding and a collapsing universes. The proper…
A special relativity based on the de Sitter group is introduced, which is the theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of…
The Dirac monopoles in 3-space and their generalization by C. N. Yang to 5-space are observed to be just the Levi-Civita spin connection of the cylindrical Riemannian metric on the 3- and 5- dimensional punctured spaces. Their…
T-Duality on a timelike circle does not interchange IIA and IIB string theories, but takes the IIA theory to a type $IIB^*$ theory and the IIB theory to a type $IIA^*$ theory. The type $II^*$ theories admit E-branes, which are the images of…
After a brief summary of Double Special Relativity (DSR), we concentrate on a five dimensional procedure, which consistently introduce coordinates and momenta in the corresponding four-dimensional phase space, via a Hamiltonian approach.…