Higher algebraic structures and quantization
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Publication:1315024
DOI10.1007/BF02102643zbMATH Open0790.58007arXivhep-th/9212115OpenAlexW2022976991MaRDI QIDQ1315024
Author name not available (Why is that?)
Publication date: 30 June 1994
Published in: (Search for Journal in Brave)
Abstract: We derive (quasi-)quantum groups in 2+1 dimensional topological field theory directly from the classical action and the path integral. Detailed computations are carried out for the Chern-Simons theory with finite gauge group. The principles behind our computations are presumably more general. We extend the classical action in a d+1 dimensional topological theory to manifolds of dimension less than d+1. We then ``construct a generalized path integral which in d+1 dimensions reduces to the standard one and in d dimensions reproduces the quantum Hilbert space. In a 2+1 dimensional topological theory the path integral over the circle is the category of representations of a quasi-quantum group. In this paper we only consider finite theories, in which the generalized path integral reduces to a finite sum. New ideas are needed to extend beyond the finite theories treated here.
Full work available at URL: https://arxiv.org/abs/hep-th/9212115
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