Higher Algebraic Structures and Quantization

Daniel S. Freed

doi:10.1007/bf02102643

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arXiv · hep-th/9212115

Higher Algebraic Structures and Quantization

Daniel S. Freed

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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.

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Daniel S. Freed. 1993-06-08. Higher Algebraic Structures and Quantization. https://doi.org/10.1007/bf02102643

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