다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

Background independent quantum gravity: A Status report

An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as ''emergent time'', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness.

Quantum Nature of the Big Bang: Improved dynamics

Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction. In cosmological models, while Einstein's equations hold to an excellent degree of approximation at low curvature, they undergo major modifications in the Planck regime: for matter satisfying the usual energy conditions, any time a curvature invariant grows to the Planck scale, quantum geometry effects dilute it, thereby resolving singularities of general relativity. Quantum geometry corrections become more sophisticated as the models become richer. In particular, in anisotropic models, there are significant changes in the dynamics of shear potentials which tame their singular behavior in striking contrast to older results on anisotropies in bouncing models. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues—e.g. the 'horizon problem'—from a new perspective. Such conceptual issues as well as potential observational consequences of the new Planck scale physics are being explored, especially within the inflationary paradigm. These considerations have given rise to a burst of activity in LQC in recent years, with contributions from quantum gravity experts, mathematical physicists and cosmologists. The goal of this review is to provide an overview of the current state of the art in LQC for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general and cosmologists who wish to apply LQC to probe modifications in the standard paradigm of the early universe. In this review, effort has been made to streamline the material so that each of these communities can read only the sections they are most interested in, without loss of continuity.

/pdf/loop-quantum-cosmology-a-status-report-1zx4841jrd.pdf

Loop Quantum Cosmology: A Status Report

Quantum fields propagating on quantum spacetime of a collapsing homogeneous dust ball explore a (semiclassical) dressed geometry. When the backreaction of the field is discarded, the classical singularity is resolved due to quantum gravity effects and is replaced by a quantum bounce on the dressed collapse background. In the presence of the backreaction, the emergent (interior) dressed geometry becomes mode-dependent which scales as radiation. Semiclassical dynamics of this so-called {\em rainbow}, dressed background is analyzed. It turns out that the backreaction effects speeds up the occurrence of the bounce in comparison to the case where only a dust fluid is present. By matching the interior and exterior regions at the boundary of dust, a mode-dependent black hole geometry emerges as the exterior spacetime. Properties of such rainbow black hole are discussed. That mode dependence causes, in particular, a chromatic aberration in gravitational lensing process of which maximal magnitude is estimated via calculation of the so-called Einstein angle.

Rainbow Black Hole From Quantum Gravitational Collapse

Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective for n-valent vertex in case when it is a map from SO(3) into SO(3)xSO(3) representations. We find, however, that the EPRL map is not isometric. In the consequence, in order to be written in a SU(2) amplitude form, the formula for the partition function has to be rederived. We do it and obtain a new, complete formula for the partition function. The result goes beyond the SU(2) spin-foam models framework.

The EPRL intertwiners and corrected partition function

There are two mathematical relativity frameworks generalizing the black hole theory: the theory of isolated horizons (IH) and the theory of near horizon geometries (NHG). We outline here and discuss the derivation of the NHG from the theory of IH by composing spacetimes from IH. The simplest but still quite general class of solutions to Einstein's equations of this type defines spacetimes foliated by Killing horizons emanating from extremal horizons. That derivation, clearly being a link between the two frameworks, seems to be unknown to the NHG researchers and is hardly acknowledged in reviews on the IH. This lecture was a contribution to the Mathematical Structures session of the 2nd LeCosPA International Symposium "Everything about Gravity" celebrating the centenary of Einstein's General Relativity on December 14-18, 2015 in Taipei.

When Isolated Horizons met Near Horizon Geometries

3rd Quantum Gravity and Quantum Geometry School

In this article we continue the work on translating elements of the perturbative quantum ﬁeld theory deﬁned on Minkowski spacetime into the background independent framework of Loop Quantum Gravity. We present the construction of r-Fock measures for SU ( N ) gauge theories and provide a relation between these new r-Fock measures and the difeomorphism invariant measure used in loop quantum gravity.

Jerzy Lewandowski

Papers

Rainbow Black Hole From Quantum Gravitational Collapse

The EPRL intertwiners and corrected partition function

When Isolated Horizons met Near Horizon Geometries

3rd Quantum Gravity and Quantum Geometry School

Loop representation and r-Fock measures for $SU(N)$ gauge theories