Related papers: The extended phase space approach to quantization …

We shortly review the state of art and perspectives of Extended Theories of Gravity.

We solve the Wheeler-DeWitt equation for {\it four}-dimensional Einstein gravity as an expansion in powers of the Planck mass by means of a heat kernel regularization. Our results suggest that in the universe with a very small radius or…

We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient…

A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…

This is a review article on quantum gravity. In section 1, the Penrose singularity theorem is proven. In section 2, the covariant quantization approach of gravity is reviewed. In section 3, an article by Hawking is reviewed that shows the…

The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…

We discuss and extend some aspects pertaining to the canonical quantisation of JT gravity in de Sitter space, including the problem of time and the construction of a Hilbert space. We then extend this discussion to other two dimensional…

I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two…

We compare three approaches to the quantization of (2+1)-dimensional gravity with a negative cosmological constant: reduced phase space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of…

Solutions to a scalar-tensor (dilaton) quantum gravity theory, interacting with quantized matter, are described. Dirac quantization is frustrated by quantal anomalies in the constraint algebra. Progress is made only after the…

We study the canonical quantization of the induced 2d-gravity and the pure gravity CGHS-model on a closed spatial section. The Wheeler-DeWitt equations are solved in (spatially homogeneous) choices of the internal time variable and the…

Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…

We consider the question of whether consistency arguments based on measurement theory show that the gravitational field must be quantized. Motivated by the argument of Eppley and Hannah, we apply a DeWitt-type measurement analysis to a…

Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…

I review discrete and continuum approaches to quantized gravity based on the covariant Feynman path integral approach.

Quantum gravity is effective in domains where both quantum effects and gravity are essential, such as in the vicinity of space-time singularities. This paper will investigate the quantization of a black-hole gravity, particularly the region…

We consider the induced $2$d-gravity in the minisuperspace approach. The general solution to the Wheeler-DeWitt equation is given in terms of different kind of Bessel functions of purely real or imaginary orders. We study the properties of…

We quantize the Hamilton equations instead of the Hamilton condition. The resulting equation has the simple form $-\D u=0$ in a fiber bundle, where the Laplacian is the Laplacian of the Wheeler-DeWitt metric provided $n\not=4$. Using then…

General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field's quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces…

A variational framework for the quantization of gravitational fields is developed based on an extension of the stationary action principle. Within this framework, the Wheeler-DeWitt equation for the gravitational wave functional is…