Related papers: Effective Dynamics from Coherent State Path Integr…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
We study numerically the solutions to the effective equations of Bianchi IX spacetimes within Loop Quantum Cosmology. We consider Bianchi IX models with and without inverse triad corrections whose matter content is a scalar field without…
This work contains a detailed qualitative analysis, in General Relativity and in Loop Quantum Cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics the dynamics of…
In this paper we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator $\hat{F}$ and result in different…
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models…
The choice of the regularization scheme in Loop Quantum Cosmology (LQC) is crucial for the predicted phenomenology. We outline how the improved scheme can be naturally realized in Quantum Reduced Loop Gravity, describing the Universe as an…
Loop quantum gravity introduces strong non-perturbative modifications to the dynamical equations in the semi-classical regime, which are responsible for various novel effects, including resolution of the classical singularity in a Friedman…
We study the evolution of a homogeneous and isotropic spacetime whose spatial sections have three-torus topology, coupled to a massless scalar field with small scalar perturbations within loop quantum cosmology. We consider a proposal for…
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…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for…
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of…
A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have…
Quantum corrections of certain types and relevant in certain regimes can be summarised in terms of an effective action calculable, in principle, from the underlying theory. The demands of symmetries, local form of terms and dimensional…
For a class of solutions of the fundamental difference equation of isotropic loop quantum cosmology, the difference equation can be replaced by a differential equation valid for {\em all} values of the triad variable. The differential…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
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…
A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and…