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Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined…
We present a new approach to quantum gravity starting from Feynman's formulation for the simplest example, that of a scalar field as the representative matter. We show that we extend his treatment to a calculable framework using resummation…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is…
We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…
The properties of the Volume operator in Loop Quantum Gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater than four. The present analysis benefits from the general…
Four-dimensional gravity admits many equivalent formulations - metric, Einstein-Cartan, teleparallel, McDowell-Mansouri, among others - each offering distinct advantages, particularly, in view of quantization. We propose a new formulation…
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…
We present a new approach to quantum general relativity based on the idea of Feynman to treat the graviton in Einstein's theory as a point particle field subject to quantum fluctuations just as any such field is in the well-known Standard…
A new canonical Hopf algebra called the quantum pseudo-K\"ahler plane is introduced. This quantum group can be viewed as a deformation quantization of the complex two-dimensional plane $\mathbb{C}^2$ with a pseudo-K\"ahler metric, or as a…
The loop representation plays an important role in canonical quantum gravity because loop variables allow a natural treatment of the constraints. In these lectures we give an elementary introduction to (i) the relevant history of loops in…
We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum…
It is well known that the quantum double structure plays an important role in three dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three dimensional…
We show that General Relativity can be formulated as a constrained topological theory for flat 2-connections associated to the Poincar\'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge…
Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL(2,C). Even though many monographs exist devoted to this theory, the different tools needed (e.g. representation theory, harmonic…
We consider the coupling between three dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
We study homogenous and isotropic quantum cosmology using the spinfoam formalism of Loop Quantum Gravity (LQG). We define a coupling of a scalar field to the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model. We…
We propose a general setting for a universal representation of the quantum structure on which quantum information stands, whose dynamical evolution (information manipulation) is based on angular momentum recoupling theory. Such scheme…