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Introduction to topological quantum field theory
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Introduction A topological quantum field theory (TQFT) is an, almost, metric independent quantum field theory that gives rise to topological invariants of the background manifold. The most well known example of a 3-dimensional TQFT is Chern-Simons-Witten theory, in which the expectation value of an observable, obtained as the product of the Wilson loops associated with a link, is the generalised Jones invariant of the link. Unfortunately the form for the invariants obtained by this procedure is that of an integral over an infinite dimensional space on which, for a mathematician, a measure is not rigorously defined. Various ways of avoiding this difficulty have been developed. These fall into two main categories, namely, formal manipulations of Witten's path integral into a form which can then be rigorously defined, and axiomatic encapsulations of the properties of TQFTs. In these notes we will be concerned with the second path, demonstrating how complex categorical and algebraic structures appear, from apparently simple geometry. As will be seen in the lecture, these structures are related to the quantum group structures which arise in other approaches. Download link：http://www.isload.com.cn/store/7o4ecbuhzctgu [ Last edited by zhq025 on 2008-1-16 at 10:23 ] |
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