Related papers: A Strichartz estimate for de Sitter space
Connection of the invariant Dirac equation over the de Sitter space with irreducible representations of the de Sitter group is ascertained. The set of solutions of this equation is obtained in the form of the product of two different…
In a recent paper [1], it has been shown that negative norm states are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content…
Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group $SO_0(1,4)$ or $Sp(2,2)$ as an appealing substitute to the flat space-time Poincare relativity. Quantum…
We prove local Strichartz estimates on compact manifolds with boundary. Our results also apply more generally to compact manifolds with Lipschitz metrics.
Graviton loop corrections to observables in de Sitter space often lead to infrared divergences. We show that these infrared divergences are resolved by the spontaneous breaking of de Sitter invariance.
In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to first and third harmonics, which leads to a reduced partial…
We consider the influence of a noncommutative space on the Klein-Gordon and the Dirac oscillators. The nonrelativistic limit is taken and the $\theta$-modified Hamiltonians are determined. The corrections of these Hamiltonians on the energy…
We establish sharp-in-time kernel and dispersive estimates for the Schr\"odinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties…
Quantum gravity in 2+1 dimensions with a positive cosmological constant can be represented as an SL(2,C) Chern-Simons gauge theory. The symmetric vacuum of this theory is a degenerate configuration for which the gauge fields and spacetime…
In this letter we show that the ``preferred'' Klein-Gordon Quantum Field Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the…
We present a complete study of a family of tachyonic scalar fields living on the de Sitter universe. We show that for an infinite set of discrete values of the negative squared mass the fields exhibit a gauge symmetry and there exists for…
In this paper we present a novel class of asymptotic consistent exponential-type integrators for Klein-Gordon-Schr\"odinger systems that capture all regimes from the slowly varying classical regime up to the highly oscillatory…
We propose that de-Sitter space-time originates from Gaussian distribution in a quantum harmonic oscillator system. This equation associates with a massless Klein-Gordon equation. We discover that every excited states of quantum oscillator…
In this paper, we consider a semiclassical version of the fractional Klein-Gordon equation on the lattice, $h{\mathbb{Z}}^n.$ Contrary to the Euclidean case that was considered in [2], the discrete fractional Klein-Gordon equation is…
The two-point function of linearized gravitons on de Sitter space is infrared divergent in the standard transverse traceless synchronous gauge defined by $k=0$ cosmological coordinates (also called conformal or Poincare coordinates). We…
Taking into account the Green-Schwarz anomaly counterterm in R-symmetry gauged $N=(1,0)$ supergravity in six dimensions, and the associated modification in the Maxwell kinetic term and potential, we observe that the theory admits…
In this paper, we give a formulation of the variational iteration method that makes it suitable for the analysis of the solutions of Klein-Gordon equations with variable coefficients. We particularly study a Klein-Gordon problem which has…
In this expository note, I present some basic geometric and twistor theoretic facts about de Sitter space leading up to a discussion of Penrose's quasi-local mass construction for linear gravity theory in the de Sitter background. The…
Strichartz estimates are derived from $\ell^2$-decoupling for phase functions satisfying a curvature condition. Bilinear refinements without loss in the high frequency are discussed. Estimates are established from uniform curvature…
We study classical, real Klein-Gordon theory on Lorentzian Anti de Sitter (AdS_{1,d}) spacetimes with spatial dimension d. We give a complete list of well defined and bounded Klein-Gordon solutions for three types of regions on AdS: slice…