Related papers: Variational Methods in Loop Quantum Cosmology
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
Field transformations for the quantum effective action lead to different pictures of a given physical situation, as describing a given evolution of the universe by different geometries. Field transformations for functional flow equations…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to…
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties…
A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the…
Loop quantum cosmology (LQC) seems to be predicting modified effective Friedmann equations without extra degrees of freedom. A puzzle arises if one decides to seek for a covariant effective action which would lead to the given Friedmann…
We analyze the cosmological solutions to the recently proposed nonlocal quantum effective action for gravity with a cosmological term. We show that the vacuum energy decays with a slow-roll parameter proportional to the anomalous…
Recently, Lloyd and Montangero have made a brief research proposal on universal quantum computation in integrable systems. The main idea is to encode qubits into quantum action variables and build up quantum gates by the method of resonant…
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…
Starting from the von Neumann equation, we construct the quantum evolution equation for the effective action for systems in mixed states. This allows us to find the hierarchy of equations which describe the time evolution of equal time…
Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…
We present some results concerning the large volume limit of loop quantum cosmology in the flat homogeneous and isotropic case. We derive the Wheeler-De Witt equation in this limit. Looking for the action from which this equation can also…
For the same quantum field theory distinct effective actions can be obtained by coupling sources to different choices of field variables. This is the same as considering effective actions for theories related by a change of variables and…
This Chapter provides an up to date, pedagogical review of some of the most relevant advances in loop quantum cosmology. We review the quantization of homogeneous cosmological models, their singularity resolution and the formulation of…
Loop quantum cosmology in (b, v) variables, which is governed by a unit step size difference equation, is embedded into a full theory context based on similar variables. A full theory context here means a theory of quantum gravity arrived…
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.
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…