Canonical Quantum Supergravity in Three Dimensions, (some lines lost during submission)

Abstract

We discuss the canonical treatment and quantization of matter coupled supergravity in three dimensions, with special emphasis on $N=2$ supergravity. We then analyze the quantum constraint algebra; certain operator ordering ambiguities are found to be absent due to local supersymmetry. We show that the supersymmetry constraints can be partially solved by a functional analog of the method of characteristics. We also consider extensions of Wilson loop integrals of the type previously found in ordinary gravity, but now with connections involving the bosonic and fermionic matter fields in addition to the gravitational connection. In a separate section of this paper, the canonical treatment and quantization of non-linear coset space sigma models are discussed in a self contained way.

40 pages, LaTeX, DESY 93-073

References in corpus (6)

• Locally supersymmetric D=3 non-linear sigma models
• The Non-perturbative Canonical Quantization of the N=1 Supergravity
• Current Algebra of Classical Non-Linear Sigma Models
• Physical states in $N=1$ supergravity
• Inconsistency of Canonically Quantized N=1 Supergravity?
• Solutions to the Wheeler DeWitt Constraint of Canonical Gravity Coupled to Scalar Matter Fields

Cited by in corpus (14)

• Background Independent Quantum Gravity: A Status Report
• Loop quantum gravity: an outside view
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Physical States in Canonically Quantized Supergravity
• Loop Quantum Gravity
• Curvature Invariants and Lower Dimensional Black Hole Horizons
• About Loop States in Supergravity
• Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
• New Canonical Variables for d=11 Supergravity
• Quaternionic Quantization Principle in General Relativity and Supergravity
• Translational invariance of the Einstein-Cartan action in any dimension
• Reduced phase space quantization of Ashtekar's gravity on de Sitter background
• Radiative Corrections in 2+1 Dimensional Supergravity
• Reality conditions for (2+1)-dimensional gravity coupled with the Dirac field