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Quantization of Chern-Simons gauge theory with complex gauge group. (English) Zbl 0717.53074
The author studies the canonical quantization of Chern-Simons gauge theory in \(2+1\) dimensions considering the case in which the gauge group is a complex Lie group. The Lagrangian is defined on a three-dimensional manifold \(M=\Sigma *{\mathbb{R}}\), with \({\mathbb{R}}'\) being the time axis and \(\Sigma\) an oriented closed surface. The special case in which \(\Sigma\) is a genus one surface is also analyzed. The quantization is described in close analogy with the compact gauge group case and the gravitational interpretation of the SL(2,\({\mathbb{C}})\) theory is also considered.
Reviewer: V.Silveira

MSC:
53C80 Applications of global differential geometry to the sciences
81T13 Yang-Mills and other gauge theories in quantum field theory
81T70 Quantization in field theory; cohomological methods
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