Related papers: Towards a "pre-canonical" quantization of gravity …
The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the…
The Chern-Weil topological theory is applied to a classical formulation of general relativity in four-dimensional spacetime. Einstein--Hilbert gravitational action is shown to be invariant with respect to a novel translation…
The stochastic quantization method is applied to the recent proposal by Ho\v{r}ava for gravity. We show that in contrast to General Relativity, the Ho\v{r}ava's action, satisfying the detailed balance condition, has a stable,…
We present the manifestly covariant quantization of quadratic gravity or higher-derivative gravity in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance on the basis of the BRST transformation. We…
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…
We perform the manifestly covariant quantization of a scale invariant gravity with a scalar field, which is equivalent to the well-known Brans-Dicke gravity via a field redefinition of the scalar field, in the de Donder gauge condition (or…
The effort to discover a quantum theory of gravity is motivated by the need to reconcile the incompatibility between quantum theory and general relativity. Here, we present an alternative approach by constructing a consistent theory of…
In this paper we extend the WKB-like `non-relativistic' expansion of the minimally coupled Klein--Gordon equation after Kiefer and Singh [1], L\"ammerzahl [2] and Giulini and Gro{\ss}ardt [3] to arbitrary order in $c^{-1}$, leading to…
The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the…
It is possible to implement a certain form of modified gravity inspired by loop quantization through non-bijective canonical transformations. The canonical nature might suggest that such modifications are guaranteed to preserve general…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
We study 2d gravity coupled to $c,1$ matter through canonical quantization of a free scalar field, with background charge, coupled to gravity. Various features of the theory can be more easily understood in the canonical approach, like…
We show that the Schr\"odinger wave functional may be obtained as the product integral of precanonical wave functions on the space of field and space-time variables. The functional derivative Schr\"odinger equation underlying the canonical…
We perform the manifestly covariant quantization of $f(R)$ gravity in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance. We explicitly calculate various equal-time commutation relations (ETCRs),…
Classical and quantum Friedmann-Lema\^itre-Robertson-Walker universes filled with non-interacting radiation and dust fluids are considered in the framework of Ho\v{r}ava-Lifshitz gravity theory. The Ho\v{r}ava-Lifshitz theory is set in its…
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…
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
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…
Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears "frozen." Two strategies towards the…