Related papers: Wheeler-DeWitt Equation in 3 + 1 Dimensions
Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
We describe a simple lattice model of higher-curvature quantum gravity in two dimensions and study the phase structure of the theory as a function of the curvature coupling. It is shown that the ensemble of flat graphs is entropically…
We discuss the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting model with analogous features to the spherically symmetric gravitational systems in 3+1 dimensions. The functional measures over the metrics and the…
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
One of the longstanding problems of modern gravitational physics is the detection of gravitational waves, for which the standard theoretical analysis relies upon the split of the space-time metric into a background metric plus perturbation.…
A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…
Wave turbulence is by nature a multiple time scale problem for which there is a natural asymptotic closure. The main result of this analytical theory is the kinetic equation that describes the long-time statistical behaviour of such…
By using the minisuperspace model for the interior metric ofstatic black holes, we solve the Wheeler-DeWitt equation to study quantum mechanics of the horizon geometry. Our basic idea is to introduce the gravitational mass and the…
The quantization of the most general Bianchi Type II geometry -with all six scale factors, as well as the lapse function and the shift vector, present- is considered. In an earlier work, a first reduction of the initial 6-dimensional…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
By regarding the vacuum as a perfect fluid with equation of state p=-rho, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom. Instead of being…
Quantum gravity is fundamentally different from the non-gravitational quantum field theories in the sense that most of the techniques derived for the latter cannot be easily extended to the former. For example, correlation functions in…
In this work, a minisuperspace model for the projectable Ho\v{r}ava-Lifshitz (HL) gravity without the detailed balance condition is investigated. The Wheeler-deWitt equation is derived and its solutions are studied and discussed for some…
A quest for phenomenological footprints of quantum gravity is among the central scientific tasks in the rising era of gravitational wave astronomy. We study gravitational wave dynamics within the noncommutative geometry framework, based on…
A crucial problem in quantum cosmology is a careful analysis of the one-loop semiclassical approximation for the wave function of the universe, after an appropriate choice of mixed boundary conditions. The results for Euclidean quantum…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
Results for the gravitational Wilson loop, in particular the area law for large loops in the strong coupling region, and the argument for an effective positive cosmological constant discussed in a previous paper, are extended to other…
A diagonal Bianchi Type III space-time is treated, both at the classical and quantum level, in the context of Horava - Lifshitz gravity. The system of the classical equations of motion is reduced to one independent Abel's equation of the…
Applying the Helmholtz Decomposition theorem to linearized General Relativity leads to a gauge-invariant formulation where the transverse-traceless part of the metric perturbation describes gravitational waves in matter. Gravitational waves…