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Loop Quantum Gravity (L.Q.G.) is one of the two most promising tentative theory for a quantum description of gravity. When applied to the entire universe, the so-called Loop Quantum Cosmology (L.Q.C.) framework offers microscopical models…
The mixed quantum-classical Liouville equation (QCLE) provides an approximate perturbative framework for describing the dynamics of systems with coupled quantum and classical degrees of freedom of disparate thermal wavelengths. The…
In this work we construct Liouville quantum gravity on an annulus in the complex plane. This construction is aimed at providing a rigorous mathematical framework to the work of theoretical physicists initiated by Polyakov in 1981. It is…
This article presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) -- a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and…
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…
We show that under certain technical assumptions, including the existence of a constant mean curvature (CMC) slice and strict positivity of the scalar field, general relativity conformally coupled to a scalar field can be quantised on a…
This thesis discusses the worldsheet geometries in the (p,q) minimal model coupled to 2D euclidean Quantum Gravity with particular focus on non-compact geometries. We first calculate the FZZT-FZZT cylinder amplitudes for all pairs of Cardy…
Existence of a minimal measurable length, as an effective cutoff in the ultraviolet regime, is a common feature of all approaches to the quantum gravity proposal. It is widely believed that this length scale will be of the order of the…
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked…
The theory of the 2-dimensional Liouville Quantum Gravity, first introduced by Polyakov in his 1981 work has become a key notion in the study of random surfaces. In a series of articles, David, Huang, Kupiainen, Rhodes and Vargas, on the…
Loop Quantum Gravity (LQG) is a theory that proposes a way to model the behavior of the spacetime in situations where its atomic characteristic arises. Among these situations, the spacetime behavior near the Big Bang or black hole's…
We prove that SLE$_\kappa$ for $\kappa \in (4,8)$ on an independent $\gamma=4/\sqrt{\kappa}$-Liouville quantum gravity (LQG) surface is uniquely characterized by the form of its LQG boundary length process and the form of the conditional…
The first chapters introduce briefly conformal theories, Moore and Seiberg polynomial equations and Gervais-Neveu quantization of Liouville theory. The next chapters present the original results of this thesis. First, the algebra of the…
A possible discrepancy has been found between the results of a neutron interferometry experiment and Quantum Mechanics. This experiment suggests that the weak equivalence principle is violated at small length scales, which quantum mechanics…
We analyze the weak-field limit of General Relativity with matter and its possible quantisations. This analysis aims towards a predictive quantum theory to provide a first-principles description of gravitational effects in macroscopic…
The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are…
We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a compact Riemann surface. We express this gravitational action in terms of finite and well-defined quantities for any value…
We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of…
For $\xi \geq 0$ and $d \geq 3$, the higher-dimensional Liouville first passage percolation (LFPP) is a random metric on $\epsilon \mathbb{Z}^d$ obtained by reweighting each vertex by $e^{\xi h_\epsilon(x)}$, where $h_\epsilon(x)$ is a…
Liouville theorem (LT) reveals robust incompressibility of distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., LT is only conditionally true (e.g., for…