Related papers: New Developments in the Spectral Asymptotics of Qu…
A quantum gravity theory which becomes renormalizable at short distances due to a spontaneous symmetry breaking of Lorentz invariance and diffeomorphism invariance is studied. A breaking of Lorentz invariance with the breaking patterns…
The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of…
It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to {\em unmeasurable} (and hence unphysical) quantities. This is because no physical quantity can…
Quantum effects are expected to modify the cosmological dynamics of the early universe while maintaining some (potentially discrete) notion of space-time structure. In one approach, loop quantum cosmology, current models are shown here to…
A calculation of the no-boundary wave-function of the universe is put forward for a spacetime with negative curvature. A semi-classical Robertson-Walker approximation is attempted and two solutions to the field equations, one Lorentzian and…
This paper studies a new set of mixed boundary conditions in Euclidean quantum gravity. These involve, in particular, Robin boundary conditions on the perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on the whole…
We present a quantization of unimodular gravity in the connection representation for a homogeneous, isotropic, and spatially flat cosmological model without matter. In this model, the wave function is governed by a Schr\"odinger-type…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
The wave function of the universe is evaluated by using the Euclidean path integral approach. As is well known, the real Euclidean path integral diverges because the Einstein-Hilbert action is not positive definite. In order to obtain a…
We obtain the spectra of codimension-2 horizon "edge" degrees of freedom for gravity and higher-spin gauge fields in de Sitter space and in the static Nariai spacetime, advancing previous Lorentzian and Euclidean analyses of one-loop…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We present a gauge-invariant treatment of singularity resolution using loop quantum gravity techniques with respect to local SU(2) transformations. Our analysis reveals many novel features of quantum geometry which were till now hidden in…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
The structure of the divergences for transverse theories of gravity is studied to one-loop order. These theories are invariant only under those diffeomorphisms that enjoy unit Jacobian determinant (TDiff), so that the determinant of the…
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…
In this paper, the Quantum Brownian motion of a point particle induced by the quantum vacuum fluctuations of a real massless scalar field in Einstein universe under Dirichlet and Neumann boundary conditions is studied. Using the Wightman…
A calculational scheme of quantum-gravitational effects on the physical quantities is proposed. The calculations are performed in 4-$\epsilon$ dimension with $1/N$-expansion scheme, where the Einstein gravity is renormalizable and it has an…
Quantum reduced loop gravity is designed to consistently study symmetry reduced systems within the loop quantum gravity framework. In particular, it bridges the gap between the effective cosmological models of loop quantum cosmology and the…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…