Canonical treatment of coset space sigma models

Matschull, H. -J.; Nicolai, H.

doi:10.1142/S0218271894000095

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Canonical treatment of coset space sigma models

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

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.