Related papers: Novel Solution of Wheeler-DeWitt Theory
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional…
The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with…
The paper is devoted to some of the difficulties which the Wheeler - DeWitt quantum geometrodynamics encountered, in particular, a strong mathematical proof that this theory is gauge-invariant, the definition of the wave function of the…
Jackiw-Teitelboim (JT) gravity in two-dimensional de Sitter space is an intriguing model for cosmological "wave functions of the universe". Its minisuperspace version already contains all physical information. The size of compact slices is…
Selection of physically meaningful solutions of the Wheeler-DeWitt equation for the wavefunction in quantum cosmology, can be attained by a reduction of the theory to the sector of true physical degrees of freedom and their canonical…
We discuss the implications of a wave function for quantum gravity, which involves nothing but 3-dimensional geometries as arguments and is invariant under general coordinate transformations. We derive an analytic wave function from the…
The wave function for the quadratic gravity theory derived from the heterotic string effective action is deduced to first order in ${{e^{-\Phi}}\over {g_4^2}}$ by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the…
The global one-dimensional quantum gravity is the model of quantum gravity which arises from the global one-dimensionality conjecture within quantum general relativity, first considered by the author in 2010 and then in 2012. In this model…
One of the unsolved issues in the quantum gravity comes from the Wheeler-DeWitt equation, which is second order functional derivative equation. In this paper, we introduce a new method to solve the Wheeler-DeWitt equation. Usually one…
The simple quantum gravity model, based on a new conjecture within the canonically quantized 3+1 general relativity, is presented. The conjecture states that matter fields are functionals of an embedding volume form only, and reduces the…
The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wavefunction solutions is such that a…
We present the Hamiltonian formulation of a relativistic point-particle coupled to Einstein gravity and its canonical quantization \`a la Wheeler-DeWitt. In the resulting quantum theory, the wave functional is a function of the particle…
A solvable 2-dimensional conformally invariant midi-superspace model for black holes is obtained by imposing spherical symmetry in 4-dimensional conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the theory is solved…
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…
There is a common expectation that the big-bang singularity must be resolved in quantum gravity but it is not clear how this can be achieved. A major obstacle here is the difficulty of interpreting wave-functions in quantum gravity. The…
One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to…
Motivated by previous works, we study semi-classical cosmological solutions and the wave function of the Wheeler-DeWitt equation in the Bose-Parker-Peleg model. We obtain the wave function of the universe satisfying the suitable boundary…
We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat…
According to the `Cosmological Central Dogma', de Sitter space can be viewed as a quantum mechanical system with a finite number of degrees of freedom, set by the horizon area. We use this assumption together with the Wheeler-DeWitt (WDW)…
We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert problem approach is used to recast the governing equations…