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The central topic of this thesis is two dimensional Quantum Gravity and its properties. The term Quantum Gravity itself is ambiguous as there are many proposals for its correct formulation and none of them have been verified experimentally.…
We describe a program for developing a canonical gravity in 2+2 dimensions (two time and two space dimensions). Our procedure is similar to the usual canonical gravity but with two times rather than just one time. Our work may be of…
The relational framework of canonical quantum gravity with non-ultralocal constraints is explored. After demonstrating the absence of anomalies, a spatially discretized version of the relational framework is introduced. This allows the…
A new version of tetrad gravity in globally hyperbolic, asymptotically flat at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is obtained by using a new parametrization of arbitrary cotetrads to define a set of…
Using the loop variable formalism as applied to a sigma model in curved target space, we give a systematic method for writing down gauge and generally covariant equations of motion for the modes of the free open string in curved space. The…
We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
We present an analysis of the gonihedric loop model, a reformulation of the two dimensional gonihedric spin model, using two different techniques. First, the usual regular lattice statistical physics problem is mapped onto a height model…
Within the twistorial parametrization of Loop Quantum Gravity we investigate the consequences of choosing a spacelike normal vector in the linear simplicity constraints. The amplitudes for the $SU(2)$ boundary states of Loop Quantum…
In this work we introduce a criterion for testing general covariance in effective quantum gravity theories. It adapts the analysis of invariance under general spacetime diffeomorphisms of the Einstein-Hilbert action to the case of effective…
We show that the quantization ambiguities of loop quantum cosmology, when considered in wider generality, can be used to produce discretionary dynamical behavior. There is an infinite dimensional space of ambiguities which parallels the…
Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the $d$ dimensional Riemann space-time. Theory of canonical transformations, which relate equivalent…
We develop a perturbation theory of four-dimensional topological 2-form gravity without cosmological constant. A 2-form and an $SU(2)$ connection 1-form are used as fundamental variables instead of metric. There is no quantum correction…
We perform a canonical analysis of the system of 2d vacuum dilatonic black holes. Our basic variables are closely tied to the spacetime geometry and we do not make the field redefinitions which have been made by other authors. We present a…
The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically…
We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum…
We examine the relationship between covariant and canonical (Ashtekar/Rovelli/Smolin) loop variables in the context of BF type topological field theories in 2+1 and 3+1 dimensions, with respective gauge groups SO(2,1) and SO(3,1). The…
In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3+1 space-time dimensions, the boundary theory lives on the 2+1-dimensional…
We present a quantum computational framework for SU(2) lattice gauge theory, leveraging continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields. We consider a ladder as well as…
We derive quantum geometric bounds in spinful systems with spin topology characterized by a single $\mathbb{Z}$ index protected by a spin gap. Our bounds provide geometric conditions on the spin topology, distinct from the known quantum…