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Journal Article

Canonical treatment of coset space sigma models


Nicolai,  H.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;
Institut für theoretische Physik;

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Matschull, H.-.-J., & Nicolai, H. (1994). Canonical treatment of coset space sigma models. International Journal of Modern Physics D, 3(1), 81-91. doi:10.1142/S0218271894000095.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-64E5-B
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.