Quantum Mechanics of Geometry

  title={Quantum Mechanics of Geometry},
  author={Abhay Ashtekar},
  journal={arXiv: General Relativity and Quantum Cosmology},
  • A. Ashtekar
  • Published 8 January 1999
  • Physics
  • arXiv: General Relativity and Quantum Cosmology
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate students in physics. As an illustrative application, I indicate how some of the detailed features of the microstructure of geometry can be tested using black hole thermodynamics. Current and future directions of research in this area are discussed. 

Gravity and the quantum

The goal of this review is to present a broad perspective on quantum gravity for non-experts. After a historical introduction, key physical problems of quantum gravity are illustrated. While there

Quantum Geometry from the Formalism of Loop Quantum Gravity

Introducing Quantum Geometry as a consequence of the quantisation procedure of loop quantum gravity. By recasting general relativity in terms of 1 2 -flat connections, specified by the Holst’s

Problems in Quantum General Relativity and Gravitation

From the early sixties a long-term scientific wave was initiated in the communities of the physical and mathematical disciplines. It was described very well by the title of the survey book (1993)

Quantum-Spacetime Phenomenology

I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide

Introduction to loop quantum gravity and cosmology

The goal of the lecture is to present a broad perspective on loop quantum gravity and cosmology for young researchers which would serve as an introduction to lectures by Rovelli and Bojowald. The

Interface of General Relativity, Quantum Physics and Statistical Mechanics: Some Recent Developments

The arena normally used in black holes thermodynamics was recently generalized to incorporate a broad class of physically interesting situations. The key idea is to replace the notion of stationary

Quantization of static space-times

By canonically quantizing the coupling model in the framework of loop quantum gravity, this work obtains a quantum theory that actually describes quantized static space-times and might shed some light on a few physical problems concerning quantum gravity.

A topological-like gravity model in a four dimensional space-time

In this work we consider a model for gravity in 4-dimensional space-time originally proposed by A. Chamseddine which may be derived by a 5-dimensional Chern-Simons theory. Its topological origin

Coupling matter to loop quantum gravity

Motivated by recent proposals on the experimental detectability of quantum gravity effects, the present thesis investigates assumptions and methods which might be used for the prediction of such

Classical and Quantum Physics of Isolated Horizons: A Brief Overview

The arena normally used in black holes thermodynamics was recently generalized to incorporate a broad class of physically interesting situations. The key idea is to replace the notion of stationary



Lectures on Non-Perturbative Canonical Gravity

Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of

Quantum geometry of isolated horizons and black hole entropy

Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting

Quantum Geometry and Black Holes

In his Ph.D. thesis, Bekenstein suggested that, for a black hole in equilibrium, a multiple of its surface gravity should be identified with its temperature and a multiple of the area of its event

LETTER TO THE EDITOR: Isolated horizons: a generalization of black hole mechanics

A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime representing a black hole which itself is in equilibrium but whose exterior

Knots and quantum gravity

The Loop Formulation of Gauge Theory and Gravity Representation Theory of Analytic Holonomy: C*-algebras The Gauss Linking Number in Quantum Gravity Vassiliev Invariants and the Loop States in

Isolated horizons: The classical phase space

A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are “isolated” near future time-like infinity or for a finite time interval. The underlying

Loops, knots, gauge theories and quantum gravity

1. Holonomies and the group of loops 2. Loop coordinates and the extended group of loops 3. The loop representation 4. Maxwell theory 5. Yang-Mills theories 6. Lattice techniques 7. Quantum gravity

Black-hole thermodynamics

To the physicist casually interested in gravitation, a black hole is a passive object that swallows anything near it and cannot be made to disgorge it; it absorbs but cannot emit. At the close of the

Diffeomorphism-invariant generalized measures on the space of connections modulo gauge transformations

The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical

Representation Theory of Analytic Holonomy C* Algebras

Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of