Related papers: Operator Product Expansion in Two-Dimensional Quan…
We propose a toy model of quantum gravity in two dimensions with Euclidean signature. The model is given by a kind of discretization which is different from the dynamical triangulation. We show that there exists a continuum limit and we can…
Coupling any interacting quantum mechanical system to gravity in one (time) dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantised, even though the gravity sector is free of any quantum…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
Two-dimensional quantum gravity with an $R^2$ term is investigated in the continuum framework. It is shown that the partition function for small area $A$ is highly suppressed by an exponential factor $exp \{ -2\pi (1-h)^2/(m^2A) \}$, where…
Remarks are given to the structure of physical states in 2D gravity coupled to $C\leq 1$ matter. The operator algebra of the discrete state operators is calculated for the theory with non-vanishing cosmological constant.
Correlation functions are ubiquitous tools in quantum field theory from both a fundamental and a practical point of view. However, up to now their use in theories of quantum gravity beyond perturbative and asymptotically flat regimes has…
Coupling any interacting quantum mechanical system to gravity in one dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantized, even though the gravity sector is free of any quantum…
In this note we show that in a two-dimensional non-commutative space the area operator is quantized, this outcome is compared with the result obtained by Loop Quantum Gravity methods.
Consider an infinite-dimensional linear space equipped with a Gaussian measure and the group $GL(\infty)$ of linear transformations that send the measure to equivalent one. Limit points of $GL(\infty)$ can be regarded as 'spreading' maps…
We give a detailed Operator Product Expansion interpretation of the results for conformal 4-point functions computed from supergravity through the AdS/CFT duality. We show that for an arbitrary scalar exchange in AdS(d+1) all the…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
We explore the quantum correlations, fidelity and quantum thermodynamics of two coupled double quantum dots containing two excess electrons. In this regard, we investigate and compare the evolution of those measures under thermal effects…
This paper establishes several new inequalities for the $A$-norm and $A$-numerical radius of operator sums in semi-Hilbertian spaces, significantly advancing the existing theory. We present two fundamental refinements of the generalized…
Two-point correlation functions of spin operators in the minimal models ${{\cal M}}_{p,p'}$ perturbed by the field $\Phi_{13}$ are studied in the framework of conformal perturbation theory. The first-order corrections for the structure…
The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix $\{\hg_{ab}(x)\}$ composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation…
We study quantum gravity in more than four dimensions by means of an exact functional flow. A non-trivial ultraviolet fixed point is found in the Einstein-Hilbert theory. It is shown that our results for the fixed point and universal…
We analyze the size and evolution of quantum fluctuations of cosmologically relevant geometric observables, in the context of the effective relational cosmological dynamics of GFT models of quantum gravity. We consider the fluctuations of…
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field…
The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincar\'e symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading…