Three Dimensional Canonical Quantum Gravity

Abstract

General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general relativity, which will later be identified with quantum observers. A precise definition of gauge symmetries and a classification of inequivalent solutions of Einstein's equations in dreibein formalism is given as well. In the quantum part the construction of the physical Hilbert space is carried out explicitly for a torus and cylinder type space manifold, which has not been done so far. Some conceptual problems of quantum gravity are discussed from the point of view of an observer sitting inside the universe.

82 pages, uses LaTeX2e and PiCTeX

References in corpus (3)

• New Loop Representations for 2+1 Gravity
• About Loop States in Supergravity
• New representation and a vacuum state for canonical quantum gravity

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• The Phase Space Structure of Multi Particle Models in 2+1 Gravity
• The 2+1 Kepler Problem and Its Quantization
• Hamiltonian formulation of tetrad gravity: three dimensional case
• Polygon model from first order gravity
• 2+1 Sector of 3+1 Gravity
• Canonical analysis of the BCEA topological matter model coupled to gravitation in (2+1) dimensions
• de Sitter Spaces
• On Special Re-quantization of a Black Hole