Related papers: On the Hydrogen Atom in the Holographic Universe
The anti-de Sitter (AdS) black hole plays an important role in the holographic principle. In this study, the upper bound in energy corresponding to the mass of the Schwarzschild black hole is modified to be that of the AdS black hole. Via…
We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The fundamental degrees of freedom are $2N$ bosonic fields living on the future…
Our Universe is expected to finally approach a de Sitter universe whose horizon is considered to be in thermal equilibrium. In the present article, both the energy stored on the horizon and its thermodynamic fluctuations are examined…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
We extend the usual Kustaanheimo-Stiefel $4D\to 3D$ mapping to study and discuss a constrained super-Wigner oscillator in four dimensions. We show that the physical hydrogen atom is the system that emerges in the bosonic sector of the…
We consider a conformally coupled scalar QFT on $2+1$ dimensional static Einstein universe $R \times S^2$, and write down the free theory Hilbert space. We explain that this theory is secretly a QFT in $2+1$ de Sitter space because all the…
In this talk we entertain the possibility that the synthesis of general covariance and quantum mechanics requires an extension of the basic kinematical setup of quantum mechanics. According to the holographic principle, regions of spacetime…
The Hamiltonian of classical anti-de Sitter gravity is a pure boundary term on-shell. If this remains true in non-perturbative quantum gravity then i) boundary observables will evolve unitarily in time and ii) the algebra of boundary…
We develop a toolbox for manipulating arrays of Rydberg atoms prepared in high-dimensional hydrogen-like manifolds in the regime of linear Stark and Zeeman effect. We exploit the SO(4) symmetry to characterize the action of static electric…
A semi-classical analysis of vacuum energy in the expanding spacetime suggests that the cosmological term decays with time, with a concomitant matter production. For early times we find, in Planck units, $\Lambda \approx H^4$, where H is…
We consider the role of high-lying Rydberg states of simple atomic systems such as $^1$H in setting constraints on physics beyond the Standard Model. We obtain highly accurate bound states energies for a hydrogen atom in the presence of an…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
A complete description of the multitudinous ways in which quantum particles can be entangled requires the use of high-dimensional abstract mathematical spaces. We report here a particularly interesting feature of the nine-dimensional convex…
We describe a scheme for constructing the holographic dual of the full D3-brane geometry with charge $K$ by embedding it into a large anti-de Sitter space of size $N$. Such a geometry is realized in a multi-center anti-de Sitter geometry…
Anti-de Sitter space in five dimensions provides an exact geometrical representation of the conformal group. Remarkably, gravity in AdS$_5$ space is holographically dual to frame-independent light-front Hamiltonian theory, derived from the…
A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2,R) group manifold. Applied to the cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to split the…
The one-state statement for closed universes has sparked considerable discussion. In this paper, we examine its physical meaning in the context of the Hartle-Hawking state and de Sitter space. We argue that the one-state property of closed…
Let $H := \begin{pmatrix} 1 & {\mathbf R} & {\mathbf R} \\ 0 & 1 &{\mathbf R} \\ 0 & 0 & 1 \end{pmatrix}$ denote the Heisenberg group with the usual Carnot-Carath\'eodory metric $d$. It is known (since the work of Pansu and Semmes) that the…
We discuss and extend some aspects pertaining to the canonical quantisation of JT gravity in de Sitter space, including the problem of time and the construction of a Hilbert space. We then extend this discussion to other two dimensional…
We study the volume of maximal globally hyperbolic Anti-de Sitter manifolds containing a closed orientable Cauchy surface $S$, in relation to some geometric invariants depending only on the two points in Teichm\"uller space of $S$ provided…