# Quantum Mechanics of Geometry

@article{Ashtekar2000QuantumMO, title={Quantum Mechanics of Geometry}, author={Abhay Ashtekar}, journal={arXiv: General Relativity and Quantum Cosmology}, year={2000}, pages={13-34} }

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.

## 35 Citations

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## References

SHOWING 1-10 OF 55 REFERENCES

### Lectures on Non-Perturbative Canonical Gravity

- Physics
- 1991

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

- Physics
- 2000

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

- Physics
- 1998

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

- Physics
- 1999

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

- Physics
- 1994

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

- PhysicsAdvances in Theoretical and Mathematical Physics
- 1999

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

- Physics
- 1996

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

- Physics
- 1980

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

- Mathematics
- 1993

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

- Mathematics
- 1993

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…