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

The small algebra of loop functionals, defined by Rovelli and Smolin, on the Ashtekar phase space of general relativity is studied. Regarded as coordinates on the phase space, the loop functionals become degenerate at certain points. All the degenerate points are found and the corresponding degeneracy is discussed. The intersection of the set of degenerate points with the real slice of the constraint surface is shown to correspond precisely the Goldberg-Kerr solutions. The evolution of the holonomy group of Ashtekar's connection is examined, and the complexification of the holonomy group is shown to be preserved under it. Thus, an observable of the gravitational field is constructed.

/pdf/degeneracy-in-loop-variables-2r8ykw3xu2.pdf

Degeneracy in Loop Variables

(This is a report for the Proceedings of ``Journees Relativistes 1993'' written in September 1993. Containes a short description of the results published elsewhere in the joint paper with A. Ashtekar) Integral calculus on the space of gauge equivalent connections is developed. By carring out a non-linear generalization of the theory of cylindrical measures on topological vector spaces, a faithfull, diffeomorphism invariant measure is introduced on a suitable completion of the quotient space. The strip (i.e. momentum) operators are densely-defined in the resulting Hilbert space and interact with the measure correctly, to become essentially self adjoint operators.

Topological Measure and Graph-Differential Geometry on the Quotient Space of Connections

A quantum reduction to spherical symmetry in loop quantum gravity

We develop the quantum theory of a scalar field on loop quantum cosmology Bianchi I geometry. In particular, by considering only the single modes of the field, the evolution equation is derived from the quantum scalar constraint: it is shown that the same equation can be obtained from quantum field theory on a ``classical'' effective geometry. We then study the dependence of this effective space-time on the wave vector of the modes (which could in principle generate a deformation in local Lorentz symmetry), by analyzing the dispersion relation for propagation of the test field on the resulting geometry. We show that when we disregard the backreaction no Lorentz violation is present, despite the effective metric being different than the classical Bianchi I. Furthermore, a preliminary analysis of the correction due to inclusion of backreaction is briefly discussed in the context of Born-Oppenheimer approximation.

Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time

A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational Dirac observables. Two cases are considered. In the first case, the spectrum of the operator $(1/2)\pi^2 B - H$ is assumed to be discrete. The quantum theory defined by the constraint takes the form of a Schroedinger-like quantum mechanics with a generalized Hamiltonian $\sqrt{B^{-1} H}$. In the second case, the spectrum is absolutely continuous and some peculiar asymptotic properties of the eigenfunctions are assumed. The resulting Hilbert space and the dynamics are characterized by a continuous family of the Schroedinger-like quantum theories. However, the relational observables mix different members of the family. Our assumptions are motivated by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases considered in the paper correspond to the negative and, respectively, positive cosmological constant. Our results should be also applicable in many other general relativistic contexts.

Jerzy Lewandowski

Papers

Degeneracy in Loop Variables

Topological Measure and Graph-Differential Geometry on the Quotient Space of Connections

A quantum reduction to spherical symmetry in loop quantum gravity

Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time

Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC