Related papers: Closed formula for the matrix elements of the volu…

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…

In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint programme. The physical inner product is expressed by using the group averaging technique for a single self-adjoint master constraint…

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…

A geometric formalism is developed which allows to describe the non-linear regime of higher-spin gravity emerging on a cosmological quantum space-time in the IKKT matrix model. The vacuum solutions are Ricci-flat up to an effective vacuum…

In loop quantum cosmology, the Hamiltonian reduces to a finite difference operator. We study the initial singularity and the large volume limit against the ambiguities in the discretisation and the operator ordering within a homogeneous,…

A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…

I review the formalism of loop quantum gravity, in both its real and complex formulations, and spin foam theory which is its path integral counterpart. Spin networks for non-compact groups are introduced (following hep-th/0205268) to deal…

In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to…

We evaluate the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity…

We introduce the Quantum Holonomy-Diffeomorphism *-algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical…

We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…

The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills…

We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…

We argue that the demand of background independence in a quantum theory of gravity calls for an extension of standard geometric quantum mechanics. We discuss a possible kinematical and dynamical generalization of the latter by way of a…

Following the same steps made for a scalar field in a parallel publication, we propose a class of perturbative theories of quantum gravity based on fractional operators, where the kinetic operator of the graviton is either made of…

A nonlocal quantum gravity theory is presented which is finite and unitary to all orders of perturbation theory. Vertex form factors in Feynman diagrams involving gravitons suppress graviton and matter vacuum fluctuation loops by…

The canonical ``loop'' formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein's theory of General Relativity. Some among the most meaningful results of the…

The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…

We advocate lattice methods as the tool of choice to constructively define a background-independent theory of Lorentzian quantum gravity and explore its physical properties in the Planckian regime. The formulation that arguably has most…

The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a…