Related papers: Eigenvalues of the volume operator in loop quantum…
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A…
An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
We propose to quantify the complexity of non-equilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of level spacing distribution of their spectra. Based on extensive numerical studies in a…
In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint programme. The physical inner product is expressed by using the group averaging technique for a single self-adjoint master constraint…
Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum…
We discuss the quantum mechanical description of a gravitational wave interacting with a cavity electromagnetic field. Quantum fluctuations of the gravitational vacuum induce squeezing in the optical field. Moreover, this squeezing…
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…
This article reviews the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops. We discuss pitfalls of several of the results and in particular discuss the issues…
The eigenvalue problem in quantum mechanics is reduced to quantization of the classical action of the physical system. State function of the system, $\psi_0(\phi)$, is written in the form of superposition of two plane waves in the phase…
We consider Robin Laplace operators on a class of two-dimensional domains with cusps. Our main results include the formula for the asymptotic distribution of the eigenvalues of such operators. In particular, we show how the eigenvalue…
The Hamiltonian constraint remains an elusive object in loop quantum gravity because its action on spinnetworks leads to changes in their corresponding graphs. As a result, calculations in loop quantum gravity are often considered…
The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the…
In this paper we provide the techniques and proofs for the resuls presented in our companion paper concerning the consistency check on volume and triad operator quantisation in Loop Quantum Gravity.
We review some work done with C. Rovelli on the use of the eigenvalues of the Dirac operator on a curved spacetime as dynamical variables, the main motivation coming from their invariance under the action of diffeomorphisms. The eigenvalues…
We compute the complete spectrum of the area operator in the loop representation of quantum gravity, using recoupling theory. This result extends previous derivations, which did not include the ``degenerate'' sector, and agrees with the…
We derive inequalities for sums of eigenvalues of Schr\"{o}dinger operators on finite intervals and tori. In the first of these cases, the inequalities converge to the classical trace formulae in the limit as the number of eigenvalues…
We construct the regularized Wheeler--De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for only a small subset of all wavefunctions being integrals of scalar densities this…
We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random…
Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's…