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Whereas the entropy of any deterministic classical system described by a principle of least action is zero, one can assign a "quantum information" to quantum mechanical degree of freedom equal to Hausdorff area of the deviation from a…
We discuss cosmological effects of the quantum loops of massless particles, which lead to temporal non-localities in the equations of motion governing the scale factor a(t). For the effects discussed here, loops cause the evolution of a(t)…
The five-dimensional loop quantum Kaluza-Klein cosmology is constructed based on the symmetric reduction of the connection formulation of the full theory. Through semiclassical analysis, the effective scalar constraint for the cosmological…
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely…
Since it is commonly believed that the observed large-scale structure of the Universe is an imprint of quantum fluctuations existing at the very early stage of its evolution, it is reasonable to pose the question: Do the effects of quantum…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under…
The spatially flat Friedman-Robertson-Walker (FRW) cosmological model with a massless scalar field in loop quantum cosmology admits a description in terms of a completely solvable model. This has been used to prove that: i) the quantum…
We show that the quantization ambiguities of loop quantum cosmology, when considered in wider generality, can be used to produce discretionary dynamical behavior. There is an infinite dimensional space of ambiguities which parallels the…
This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how…
Quantum treatment of physical reference frame leads to the Ricci flow of quantum spacetime, which is a quite rigid framework to quantum and renormalization effect of gravity. The theory has a low characteristic energy scale described by a…
Starting from an heuristic approach to the semiclassical limit in loop quantum gravity, the construction of effective Hamiltonians describing Planck length corrections to the propagation of photons and spin 1/2 fermions, leading to modified…
We give a formulation of quantum cosmology with a pressureless dust and arbitrary additional matter fields. The system has the property that its Hamiltonian constraint is linear in the dust momentum. This feature provides a natural time…
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…
The quantum model of homogeneous and isotropic universe filled with the uniform scalar field is considered. This model predicts effective inverse square-law dependence of the mean total energy density <\rho> on the expectation value of…
Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty…
We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…
The noncommutativity of the space-time had important implications for the very early Universe, when its size was of the order of the Planck length. An important implication of this effect is the deformation of the standard dispersion…
Within some approaches to loop quantum cosmology, the existence of an Euclidean phase at high density has been suggested. In this article, we try to explain clearly what are the observable consequences of this possible disappearance of…