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[资源] Introduction to topological quantum field theory

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.

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[ Last edited by zhq025 on 2008-1-16 at 10:23 ]

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