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A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
We show that Euclidean 3D-gravity coupled to a Gaussian scalar massive matter field in first-order dreibein formalism gives a quantum theory which has a finite perturbative expansion around a non-vanishing background. We also discuss a…
The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…
Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and…
We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
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…
Non-linear cosmic structures contain valuable information on the expansion history of the background space-time, the nature of dark matter, and the gravitational interaction. The recently developed kinetic field theory of cosmic structure…
A covariant scheme for matter coupling with a GL(3,R) gauge formulation of gravity is studied. We revisit a known Yang-Mills type construction, where quadratical power of cosmological constant have to be considered in consistence with…
General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory…
This research establishes an operational measurement way to express the quantum field theory in a geometrical form. In four-dimensional spacetime continuum, the orthogonal rotation is defined. It forms two sets of equations: one set is…
Recently a class of alternative theories of gravity which goes under the name f(R) gravity, has received considerable attention, mainly due to its interesting applications in cosmology. However, the phenomenology of such theories is not…
We construct a topological field theory which, on the one hand, generalizes BF theories in that there is non-trivial coupling to `topological matter fields'; and, on the other, generalizes the three-dimensional model of Carlip and Gegenberg…
We will highlight that despite there being various approaches to quantum gravity, there are universal approach-independent features of quantum gravity. The geometry of spacetime becomes an emergent structure, which emerges from some purely…
We introduce the framework of Hopf algebra field theory (HAFT) which generalizes the notion of group field theory to the quantum group (Hopf algebra) case. We focus in particular on the 3d case and show how the HAFT we considered is…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes…